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