The algebraic unknotting number of a knot is the minimal number of crossing changes required to convert a knot into a knot with Alexander polynomial 1.
[1] Borodzik, Maciej; Friedl, Stefan. On the algebraic unknotting number. Trans. London Math. Soc. 1 (2014), no. 1, 57--84. arxiv
[2] H. Murakami, Algebraic Unknotting Operation, Q&A. Gen. Topology 8 (1990), 283-292.