by Stepan Orevkov and Vsevolod Shevchishin
It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses. The proof is a parametric version of the Bennequin's proof of the fact that any transversal link is transversally isotopic to a closed braid.
The extended version of the paper is supplied with an appendix, where
we derive the classical Markov theorem from our result.