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We first study the degeneration of a sequence of Hermitian-Yang-Mills metricswith respect to a sequence of balanced metrics on a Calabi-Yau threefold$\hat{X}$ that degenerates to the balanced metric constructed by Fu, Li, andYau on the complement of finitely many (-1,-1)-curves in $\hat{X}$. Then undersome assumptions we show the existence of Hermitian-Yang-Mills metrics onbundles over a family of threefolds $X_t$ with trivial canonical bundlesobtained by performing conifold transitions on $\hat{X}$.

Existence of Hermitian-Yang-Mills metrics under conifold transitions