A pass-move and a -move are local moves on oriented links defined by L. H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self -equivalent) if one can be deformed into the other by pass-moves (resp. #-moves), where none of them can occur between distinct components of the link. These relations are equivalence relations on ordered oriented links and stronger than link-homotopy defined by J. Milnor. We give two complete classifications of links with arbitrarily many components up to self pass-equivalence and up to self -equivalence respectively. So our classifications give subdivisions of link-homotopy classes.
"Classification of links up to self pass-move." J. Math. Soc. Japan 55 (4) 939 - 946, October, 2003. https://doi.org/10.2969/jmsj/1191418757