We show that surgery on a connected clover (or clasper) with at least one loop preserves the concordance class of a knot. Surgery on a slightly more special class of clovers preserves invertible concordance. We also show that the converse is false. Similar results hold for clovers with at least two loops vs. –equivalence.
"Concordance and 1–loop clovers." Algebr. Geom. Topol. 1 (2) 687 - 697, 2001. https://doi.org/10.2140/agt.2001.1.687