I'm too lazy to go through this frame by frame, but the seamlessness of it has more to do with matching camera movements from shot to shot. One shot pans into the next, another shot tilts into the next. It looks like a very fast cross dissolve, or maybe a non/additive dissolve.
Pretty much, just some planning. It's simple to do, you just need to know that you want to do it when you're on location.
It's a whip pan (or in some cases, tilt) transition from what I can see. You do a really quick pan or tilt at the end of one shot, the pick it up with a whip pan or tilt in the beginning of the next shot. You don't even have to do it all that fast, as you can see from those clips. Add a quick cross dissolve during the time that the camera is being moved for the transition. The motion blur helps to mask the dissolve.
You can clearly see the dissolve going on in this frame (from 42 seconds)