Stability of the tangent bundle through conifold transitions

Let X be a compact, Kahler, Calabi-Yau threefold and suppose X ?X_?Xt$X\mapsto \underline{X}\leadsto X_t$ , for t & ISIN;& UDelta;$t\in \Delta$, is a conifold transition obtained by contracting finitely many disjoint (-1,-1)$(-1,-1)$ curves in X and then smoothing the resulting ordinary double point singularities. We show that, for |t|MUCH LESS-THAN1$|t|\ll 1$ sufficiently small, the tangent bundle T1,0Xt$T<^>{1,0}X_{t}$ admits a Hermitian-Yang-Mills metric Ht$H_t$ with respect to the conformally balanced metrics constructed by Fu-Li-Yau. Furthermore, we describe the behavior of Ht$H_t$ near the vanishing cycles of Xt$X_t$ as t & RARR;0$t\rightarrow 0$.