Let $\mathcal{X}\rightarrow D$ be a toric degeneration, with dual intersection complex $(B,\mathscr{P})$. Then there is an open set $U\subseteq B$ such that $B\setminus U$ retracts onto the discriminant locus $\Gamma$ of $B$, and an open subset $\mathscr{U}_{t}$ of $\mathcal{X}_{t}$ which is biholomorphic to a small deformation of a twist of $X_{\epsilon}(U)$, where $\epsilon=O(-1/\ln|t|)$.