Hi, sorry I don't check here much :) Anyway, pretty much all I did was have a certain amount of "segments" there, placed in a regular circle fastion. And all I needed them to do is turn 180 degrees from "the start to the end" of the circle along their local "forward" axis. Thats the general idea, no need to overcomplicate things, just realize what mobius is and then just rotate the individual parts according to it.
In the end, there are some other animation-like factors in play to make it more appealing, like the whole strip being inclined a little bit and rotating around vertical axis, camera slowly rotating as well, and the fact that I wanted the ball to always be "on top of the strip" (above it in Y), so I rotate the segments according to current balls position, the ball pretty much dictates "where the start of the circle is".