Let $X\to \Delta$ be a flat family of complex surfaces with at most a finite number of singularities of simple type, where $\Delta$ is a complex domain in $\mathbb C$.

Here simple type means rational double point.

By a result of Tyurina, it is know that such deformations admit locally simultaneous resolutions after passing to a sufficiently high ramified cover of the base.

Conversely if $Y\to\Delta$ is a smooth family of complex surfaces and the central fiber $Y_0$ is the minimal resolution $Y_0\to X_0$ of a complex surface with a finite number of simple singularities, can we say that $Y\to \Delta$ must be (locally) a simultaneous resolution of some flat deformation of $X_0$ ?

I guess this boils down to ask whether it is possible to contract the exceptional curves of $Y_0$ within the family $Y\to\Delta$...