Distinguishing between exotic symplectic structures

We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish between two examples based on those considered by Maydanskiy and Seidel, even though their classical symplectic invariants such as symplectic cohomology vanish. We also exhibit, for any n, an exact symplectic manifold with n distinct but exotic symplectic structures, which again cannot be distinguished by symplectic cohomology.