I believe the effects you are pointing to are whats called bloom transitions. Quite a few different varieties (I usually come up with new ideas when I want to use it in work projects and it looks like a couple different techniques were used in that video).
The primary way to do them would be to animate exposure and possibly levels, increase exposure to the cut then decrease it. you can kind of pile on from there as needed, adding a blur just before the exposure makes it look like a camera aperture effect, and one shot in the video looks like a color solid was added (in a dodge layer mode it looked like) then the transition on top of that (the scene looked dark so probably wasn't getting a nice bloom so the color solid helped brighten the scene).
It's easiest in a compositor (after effects probably used here) but it is possible in an editor I'm sure, with perhaps an adjustment layer and exposure controls...best not to mess with source so you can still easily adjust the cuts. You may also see (experiment!) with adding a light glow (depending on the scene). And of course a blur if you want that effect to it as well.
Hope this helps! If you look up 'bloom transition' you will find a lot of stuff talking about plug-ins. If you find free ones, give them a try if you want. I usually do these in AE so I'm not positive how well it would work in Vegas...