A conifold transition is a surgery on a (real) six-dimensional manifold $X$
which replaces a three-sphere with trivial normal bundle by a two-sphere with
trivial normal bundle, cutting out $S^3 × D^3$ and replacing it with $D^4 × S^2$.






 [Miles Reid][1] conjectured that the moduli
space of Calabi-Yau spaces $\mathscr M_{CY}$ is connected after allowing the conifold transitions
, i.e., both resolutions/contractions and deformations/degeneration. Is there any progress about this conjecture (what about in higher dimension), A reference or information is welcomed 


  [1]: https://arxiv.org/pdf/0904.4487.pdf