My decision to rotate or invert depends on the tank type. Theoretically, tanks should not leak when inverted, however, some do leak chemicals. For leaky tanks, I rotate. For non-leaky ones, I prefer to invert for better chemical circulation. Whichever way one chooses to do it, trial and error is unavoidable for the first few attempts. Subsequently, stick to the method that gives the best result.
There are many variables: 1) No. of seconds for initial agitation time - some do it 30s some 60s, 2) Subsequent agitation 30s apart, sometimes 60s, and 3) No of turns or inversions.
As to the equivalent number of turns to one inversion, maybe there's no lab or scientific documents on it. What I normally do is, make 5 rotations followed by shaking the tank from side to side to dislodge air bubbles. That to me, is equivalent to 2 inversions.
Just sharing...