  Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya, it
is known that on a 4-manifold with boundary Stein structures with
non-isomorphic Spinc structures induce contact structures with distinct
Ozsvath-Szabo invariants. Here we give an infinite family of examples showing
that converse of Lisca-Matic-Plamenevskaya theorem does not hold in general.
Our examples arise from Mazur type corks.
