  We prove that transverse links in any contact manifold $(M,\xi)$ can be
realized as a sub-binding of a compatible open book decomposition. We define
the support genus of a transverse link and prove that the support genus of a
transverse knot is zero if there is an overtwisted disk disjoint from it. Next,
we find a relationship between the support genus of a transverse link and its
Legendrian approximation.
