It isn’t an easy transition to do in Avid, but it can be done.
The first transition in the piece could be done like this–shot 1 on V2, shot 2 (the guy crumpling the paper) on V1. They overlap by about 4 or 5 frames, depending on how fast your guy is crumpling the paper.
Start by adding a resize affect to your V2 layer. About 2 frames before you want to go to the paper crumpling, keyframe the resize on the V2 layer so your layer gets a little bigger. Add a blur plugin and put a slight blur on it to simulate motion blur. Now try a warp plugin so your shot is pulled toward the center of where the paper is being crumpled. You’ll want to use a corner pin effect, keyframed so the corner of your V2 shot follows the corners of your paper as it’s pushed together. You say you’re on media composer–if parts of the paper overlap and should be blocking your V2 shot, use animatte the cut out your V2 layer, exposing your V1 paper. Continue to up your blur a little bit, and possibly add a color effect so your V2 shot becomes a little washed out and desaturated. In the video you linked the first transition at 2:47 is very very fast. You could easily size up, add a bit of blur, warp towards the center of the crumpled paper, corner pin for about 3 or 4 frames while the paper comes together and add a 3 frame dissolve at the end. It doesn’t have to be perfect–just good enough to fool the eye at full speed playback.
Can you post an example of the clips you have that you’re trying to transition from? It would be easier to give tips is we say exactly what footage you had to work with.
Hope this helps get you started. Post back with more questions.
Mike.