Near Sizedoku

Lots of Sudoku variants include some sort of extra clues based on the sizes of adjacent numbers.  In this puzzle arrows point from larger to smaller numbers in each three-by-three cage, but only when the larger number is exactly 1, 2, or 3 more than the smaller number.  Since arrows only appear when numbers are close, we can call this a Near Sizedoku.  Remember that arrows appear whenever possible, so lack of an arrow between adjacent cells in a cage also reveals some information.  For an example, this is one possibility for this three-by-three cage:

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