I see more of this, " I visited four countries over the period of 4 years." Which I certainly believe must be the correct version. first off, 'over the period' means,summation of a period of time. So I see no reason someone should section the period of time already merged,especially when the expression has to do with 'over the period'

I see more of sentences like "I visited four countries over the period of 4 years", which, I certainly believe, must be the correct version.

First off, 'over the period' means summation of a period of time. So I see no reason someone should section the period of time already merged, especially when the expression has to do with 'over the period'.