The term "Reaching the Varanasi" itself has a deep yogic significance. It is described in Vedas itself. Actually the term Varanasi means "beyond nose". Naasi = Nose in Sanskrit and it is implying to reach the area which is beyond nose (ie. Middle of the eyebrow) ie. Ajna Chakra. Hence Vedas State who reach Ajna Chakra (middle of eyebrow) their liberation is granted.
This is explained very well in Jabala Upanishad which is a part of Shukla YajurVeda. Regarding Authenticity of Jabala Upanishad it is a pretty much authentic Upanishad. It is quoted several times in Brahma Sutra Bhasya by Adi Shankara. For eg in Brahma Sutra Bhasya 1.2.32, 2.1.3, 3.3.37-41, 3.4.17-18 and other places.
Particularly in commentary of Brahma Sutra Bhasya 1.2.32, Adi Shankara quotes:
आत्मनन्ति चैनं परमेश्वरमस्मिन्मूर्धचुबुकान्तराले जाबाला - " य एषोऽनन्तोऽव्यक्त आत्मा तं कथमहं विजानीयामिति ॥ स होवाच याज्ञवल्क्यः सोऽविमुक्त उपास्यो य एषोऽनन्तोऽव्यक्त आत्मा सोऽविमुक्ते प्रतिष्ठित इति ॥ का वै वरणा का च नाशीति सर्वानिन्द्रियकृतान्दोषान्वारयतीति तेन वरणा भवति ॥
सर्वानिन्द्रियकृतान्पापान्नाशयतीति तेन नाशी भवतीति ॥
इति वरणानासीति निरुच्य, पुनरप्यामनन्ति - "कतमं चास्य स्थानं भवतीति । भ्रुवोर्घ्राणस्य च यः सन्धिः स एष द्यौर्लोकस्य परस्य च सन्धिर्भवतीति"...... तस्मात्परमेश्वरो वैश्वानर इति सिद्धम् ।
Moreover the Gâbâlas speak in their text of the highest Lord as being in the interstice between the top of the head and the chin. 'The unevolved infinite Self abides in the avimukta (i.e. the non-released soul). Where does that Avimukta abide? It abides in the Varanâ and the Nâsî, in the middle. What is that Varanâ, what is that Nâsî?' The text thereupon etymologises the term Varanâ as that which wards off (vârayati) all evil done by the senses, and the term Nâsî as that which destroys (nâsayati) all evil done by the senses; and then continues, 'And what is its place?--The place where the eyebrows and the nose join. That is the joining place of the heavenly world (represented by the upper part of the head) and of the other (i.e. the earthly world represented by the chin).' (Gâbâla Up. I.)--Thus it appears that the scriptural statement which ascribes to the highest Lord the measure of a span is appropriate ......... By all this it is proved that Vaisvânara is the highest Lord.
Actually the above statement quoted by Adi Shankara is from the Jabala Upanishad.
We now see from Jabala Upanishad, to know the actual Yogic meaning of "Reaching of Varanasi." and how one gets liberation on reaching Varanasi.
Sage Atri asks the questions to Yajnavalkya that how can one realize self. Yajnavalkya replies that it is by worshipping Avimukta (a form of Lord Shiva).
अथ हैनमत्रिः पप्रच्छ याज्ञवल्क्यं य एषोऽनन्तोऽव्यक्त
आत्मा तं कथमहं विजानीयामिति ॥ स होवाच याज्ञवल्क्यः सोऽविमुक्त उपास्यो य एषोऽनन्तोऽव्यक्त आत्मा सोऽविमुक्ते प्रतिष्ठित इति ॥ (Jabala Upanishad 2.1)
Thereafter the sage Atri asked of Yajnavalkya: ‘How am I to realize the Self which is infinite and unmanifest ?’ (To this) Yajnavalkya replied: That Avimukta is to be worshipped; the Self which is infinite and unmanifest, is established in (i.e., is non-different from) the Avimukta.
Then again question is asked "Where does that Avimukta resides?" Then it is told he resides in Varanasi. Then the yogic meaning of Varanasi is explained.
सोऽविमुक्तः कस्मिन्प्रतिष्ठित इति । वरणायां नाश्यां च
मध्ये प्रतिष्ठित इति ॥ का वै वरणा का च नाशीति ।
सर्वानिन्द्रियकृतान्दोषान्वारयतीति तेन वरणा भवति ॥
सर्वानिन्द्रियकृतान्पापान्नाशयतीति तेन नाशी भवतीति ॥
कतमं चास्य स्थानं भवतीति । भ्रुवोर्घ्राणस्य च यः
सन्धिः स एष द्यौर्लोकस्य परस्य च सन्धिर्भवतीति । एतद्वै
सन्धिं सन्ध्यां ब्रह्मविद उपासत इति । सोऽविमुक्त उपास्य इति। सोऽविमुक्तं ज्ञानमाचष्टे । यो वैतदेवं वेदेति ॥ Jabala Upanishad 2.2 ॥
‘Which is that (place) where Avimukta is established ?’ ‘He is established in between Varana and Nasi’. ‘What is (meant by) Varana and what (by) Nasi ?’ ‘The varana is so called as it wards off all the faults committed by the (ten) organs (of perception and action). The nasi is so named as it destroys all sins committed by the (ten) organs. (The place between the varana and the nasi is the meeting place of the upper part of the nose and the centre of the eye brows). ‘Which is the seat of that (Avimukta) ?’ ‘That, which is the (well known) juncture of the eye brows and the nose, is the juncture of heaven and this world. The knowers of the Veda worship indeed this juncture as Sandhya (in their daily worship). That Avimukta is to be worshipped. He who knows this thus (the true nature of the Avimukta), imparts the wisdom of the Avimukta.
Previously it is also told how one gets liberation on reaching there:
अत्र हि जन्तोः प्राणेषूत्क्रममाणेषु रुद्रस्तारकं ब्रह्म
व्याचष्टे येनासावमृती भूत्वा मोक्षी भवति
तस्मादविमुक्तमेव निषेवेत अविमुक्तं न
विमुञ्चेदेवमेवैतद्याज्ञवल्क्यः ॥ १॥
This is the spot where, when the vital airs depart from the living person, Rudra imparts the Taraka Brahman to him by which, becoming immortal, he attains liberation (final beatitude). Hence one shall resort to the Avimukta; shall not desert the Avimukta. (Brihaspati approved of the statement saying): ‘So it is, Yajnavalkya’, verily it is so, O, revered one ! ‘It is so Yajnavalkya’.
Thus reaching the Varanasi is not a easy task in yogic sense. One has to realize the Ajna Chakra (region between eyebrow). Or one who raises Kundalini upto Ajna Chakra actually reaches there. And thus his liberation is also granted.
However this Varanasi of body corresponds to the holy region of Varanasi of earth. Here also Shiva grants liberation to those who reaches here (middle of eyebrow). There also Shiva grants liberation to those who reaches there (devotionally). Here also Rudra gives Tarak Brahman, Omkara and there also the same. Here also Avimukta (a form of Lord Shiva) resides, there also Avimukta resides. Here also it is in form as supported by Trident (actually Only susmna reaches Sahasrara, Ida and Pingala join at Ajna Chakra and thus form a trident like area), there also it is situated in Trident held by Lord Shiva.
Thus the Varanasi of our body corresponds to that Varanasi of Macro World. Thus in Yogic sense "Reaching the Varanasi" means reaching the Ajna Chakra (area beyond nose and middle of eyebrow).