Basically, there is a transition created by New Blue FX called "Roll" which you can use on Sony Vegas.
If you are unsure what this Roll transition is, here are a few examples of what it looks like...
There are numerous amounts of these Roll transitions by New Blue FX such as "Blur Up/Down/Left/Right". So I assuming that the transition is blurring the clips as it slides them across the screen, however, what blur are they using also??