With variable bitrate compression, transitions can add slightly to compressed file sizes, particularly if they have lots of motion, like a push or slide. Wipes, which don't have motion except for the edge between old and new, don't usually have this affect. Constant bitrate compression will have the same file size, but will have more artifacts around transitions that move a lot.
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When making video for ther web, cuts only without fades and fancy transistions produces the best quality streaming video. The transistions are difficult to reproduce compressed. I do use a fade here and there, but for web video cuts only is the better quality way.