K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11, author = {Akira Yasuhara}, title = {Brunnian local moves of knots and Vassiliev invariants}, journal = {Fundamenta Mathematicae}, volume = {189}, year = {2006}, pages = {289-297}, zbl = {1095.57010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11} }
Akira Yasuhara. Brunnian local moves of knots and Vassiliev invariants. Fundamenta Mathematicae, Tome 189 (2006) pp. 289-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm190-0-11/