Balanced metrics on non-Kahler Calabi-Yau threefolds

We construct balanced metrics on the family of non-Kahler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on Kahler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of $kgeq 2$ copies of $S^3times S^3$.