Classification of links up to one-two-way pass-move

We define a local move for links called the one-two-way pass-move, abbreviated briefly as the 1-2-move. The 1-2-move is motivated from the pass-move and the #-move, and it is a hybrid of them. We give a complete classification of links up to 1-2-move. In fact, we show that the equivalence under the 1-2-move is the same as that of the pass-move. On the other hand, we show that the number of 1-2-moves behaves differently from the number of pass-moves.