Let $\pi:\mathcal{X} \to S$ be a family of smooth surfaces containing contractible curves. By simultaneously blowing down the contractible curves in the family $\mathcal{X}$, we mean a family of surfaces $\pi':\mathcal{Y} \to S$ such  that 
none of the fibers contain any contractible curve and there exists a proper $S$-morphism from $\mathcal{X}$ to $\mathcal{Y}$ which is the blow-up of $\mathcal{Y}$ at the contracted points (the points to which the contractible curves map to). The question is under what condition on $\pi$ or $\mathcal{X}$ does there exist such a family $\mathcal{Y}$ as above?