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 $Y\to\Delta$...



Simultaneous resolutions and deformations of simple singularities
I think that the paper Burns-Wahl "Local contributions... " gives some of the examples you are looking for. 


(sorry I just wanted to add a comment above, but I am not sure how to do it). 


