Deformation to a conifold transition

Let $T(Y,\overline{Y},\widetilde{Y})$ be a geometric transition satisfying a good condition, for example that its birational morphism $\phi$ contracts $k$ exceptional divisors to a smooth curve of genus $g>1$ whose points are $cA_k$ singularities. Deformation-to-conifold conjecture. The transition can be deformed to a conifold transition $T'(Y',\overline{Y}',\widetilde{Y})$ as in the source's diagram. The claim is used to explain how non-conifold reverse transitions could coexist with the reverse conifold conjecture; no general proof is given.