On pass-moves and ♯-moves

We consider the two types of local moves called a pass-move and a [Formula: see text]-move. We show that the minimal number of [Formula: see text]-moves which realize a pass-move is two. We also give a pair of links which are mutually deformed by one pass-move and by one [Formula: see text]-move. Further, we study the sets of links obtained by pass-moves and [Formula: see text]-moves from a given link, and the additivity of the pass- and [Formula: see text]-Gordian distance for several sums. Finally, we give a table of pass- and [Formula: see text]-unknotting number of all prime knots up to crossing number nine except two knots.