  Suppose that a complex manifold M is locally embedded into a
higher-dimensional neighbourhood as a submanifold. We show that, if the local
neighbourhood germs are compatible in a suitable sense, then they glue together
to give a global neighbourhood of M. As an application, we prove a global
version of Hertling--Manin's unfolding theorem for germs of TEP structures;
this has applications in the study of quantum cohomology.
