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In this short note, we show that given a special K\"ahler-Einsteindegeneration with bounded geometry, for any noncentral fiber, there exists aK\"ahler-Ricci flow which converges to the K\"ahler-Einstein metric of thecentral fiber. As an example, Tian's deformations \cite{Tian97} of the Mukai3-fold admit K\"ahler-Ricci flows which converge to Donaldson'sK\"ahler-Einstein metric \cite{Don08} over the Mukai 3-fold.

On the K\"ahler-Ricci flows near the Mukai-Umemura 3-fold