When you create a snapshot, the original disk image is "frozen" in a consistent state, and all write accesses from then on will go to a new differential image. Even worse, as explained here and here, the differential image has the form of a change log, that records every change made to a file since the snapshot was taken. This means, that read accesses would have to read not only one file, but also all difference data (the original data plus every change made to the original data). The number increases even more when you cascade snapshots.
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