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I don't have any idea on how Saptarṣi constellation passes from one nakshatra to another. Consider the following lines from

When the great sages of the Saptarṣi constellation pass from Maghā to Pūrvāsāḍhā, Kali will have his full strength, beginning from King Nanda and his dynasty.

[32, 2, 12, Bhāgavata Purāṇa]

It says that Nanda dynasty was started when Saptarṣi constellation passed from Maghā to Pūrvāsāḍhā.

I want to know about the frequency of the aforementioned transition. In how many years does this happen generally?

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    Nice question. You can find the answer in the Srimad Bhagavatham itself. Also almost the exact same Sanskrit verses are contained in the Vishnu Purana. See SB 12.2.26. In this the translation of 1050 is wrong it’s 1015- as done correctly in the Vishnu Purana. The Saptarshis take 100 years in each nakshatra as per SB 12.2.27-28. Magha to Purvashadha is 10 nakshatras = 10*100 years=1000. Also Kashmiri Pandits apparently use the Saptarshi calendar - don’t have reference for this. I read on Wikipedia.
    – Adiyarkku
    Nov 30, 2020 at 16:28

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Because of the earth's axial precession (change in the orientation of the earth's axis), the location of the north pole changes slowly over time. It describes a small circle in the North over a period of 26,000 years or so. As a result, different stars are pole stars at different times. For instance, right now, Polaris is the pole star. Around the year 2800 B.C., Thuban was the pole star. Around the year 12,000 B.C. Vega was the pole star. And so on. Because of this, the saptarishi mandal is longitudinally aligned with different sets of nakshatras at different times. It seems to swing back and forth between Chitrā and Punarvasu as far as I can see (see screenshots from Stellarium below). But Pūrvāsāḍhā is on the other side of the sky, so it seems somewhat unlikely that the Saptarishi mandal would ever be aligned with it. But I may be wrong...
enter image description here

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