Abstract: It is now well-known that two birationally equivalent hyperkähler manifolds must belong to the same deformation family, as complex manifolds. This property is known to fail for other classes of varieties with trivial first Chern class, such as Calabi?Yau threefolds. In this talk, I will report on joint work in progress with Isabel Stenger and Long Wang, where we investigate a rather dramatic failure of that property. I?ll introduce a specific Calabi?Yau threefold introduced by Schoen and studied by Namikawa and Grassi?Morrison in the early 90s. I will then recount how this threefold has many non-isomorphic birational models with interesting geometric features. At last, my goal is to explain how these birational geometric features can be used to distinguish between many deformation types.