In Contact 3-manifolds, twenty years since J. Martinet’s work, Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic through contact structures if and only if they are homotopic as 2-plane fields. We provide an alternative proof of this theorem using the convex surface theory and bypasses.
"A proof of the classification theorem of overtwisted contact structures via convex surface theory." J. Symplectic Geom. 11 (4) 563 - 601, December 2013.