what does it mean to insert a char? - we move down in the matrix (number of edits increases, number of matched chars stays the same)
what does it mean to delete a char? - we move down and right in the matrix without consuming an input char (so it's an epsilon transition)
what does it mean to replace a char? we move down and right while consuming
and what does it mean to match an input char without an edit? - we just move right