Transverse stabilization in dim>3 contact topology

We'll define stabilization for codim=2 contact manifolds of dim>3 contact manifolds so that the following holds: A contact manifold is overtwisted iff its "standard contact unknot" is a stabilization. This means that many dim=2n+1>3 contact manifolds contain dim=2n-1 spheres which are unknotted smoothly but "knotted" from a contact-topological point of view.