Do you play rapid to warm up for blitz, or play blitz to open of your rapid?

Neither because both have subtle enough differences to be their own time control. I wouldn't burn out your brain power on an early chess game prior to another game; before an important chess game, chess is one of the last things on my mind. This helps rejuvenate yourself for the chess thinking required ahead. Do something preferably non-chess related and refresh yourself for your game(s) ahead. Play some pinball, cardistry, read a non-chess book (all of these I've either done myself or know someone whom has done so prior to chess), but I wouldn't recommend anything "chess-heavy." I believe one of the worst things you can do is play an off-hand game of similar time control to the one you are about to play, or to read a chess book prior to the game; you won't cram new lines into your repertoire without prior line experimentation, so why burn your mind out before the chess to come? (p.s. I see many tournament players make this mistake of reading chess books before they play, but I don't find this in their favor)

If you are still really eager for some chess "warm up" - then perhaps solve a few puzzles or tactics. This is common, but I wouldn't "think chess-related" much more deeply than that: save it for your "real game." 

Sometimes players in the tournament hall may play off-hand blitz between rounds (I've done so myself occasionally). However, this is more something fun to pass a little time and not "think" about chess the same way: this can still be risky though. I think blitz is all right if you can mentally accept it as a fun way to pass the time and not much more, but blitz is not what you want if you can't mentally make this distinction from an "important game": what you do not want is to get "too into" the blitz and then have the quick thinking carry over into a classical time control game you have next round. Plus, observers may be looking at your opening repertoire in your blitz and possibly anticipate it for a longer time control game against them later on.