Gromov-Hausdorff continuity of non-Kähler Calabi-Yau conifold transitions

We study the geometry of Calabi-Yau conifold transitions. This deformation process is known to possibly connect a Kähler threefold to a non-Kähler threefold. We use balanced and Hermitian-Yang-Mills metrics to geometrize the conifold transition and show that the whole operation is continuous in the Gromov-Hausdorff topology.