You can tell when the parts change because the music changes a bit...
The first part ends after the choir thing, the second ends when they get to that slow guitar/piano trade-off thing, the third part ends during the break between vocal parts, the fourth part ends with the solo after the vocals, the fifth part starts when the music gets into that uber-cool/heavier riff, the sixth part starts after the vocals when Romeo and Pinella get into all those solo duels, and the final part begins when with the slow guitar/piano tradeoff from the beginning...
I think that's how it goes. For a bit of easier referance, check out the live album, where they stop for a second in between parts...