Abstract: The so-called "Reid's fantasy" conjectures that Calabi-Yau 3-folds are connected together via certain geometric transitions which, in particular, will leave the Kähler world. It is expected that this picture can be realised more geometrically by equipping such spaces with canonical metric structures. In the Kähler case, the Kähler Ricci-flat metrics (given by Yau's solution of the Calabi Conjecture) provide very natural best metric structures, but it is not fully clear yet how to generalize these metrics in the non-Kähler situation. In this talk, I will present a construction via gluing technique of families of balanced Chern-Ricci flat metrics on non-Kähler small resolutions of singular nodal Calabi-Yau 3-folds which, in particular, provide solutions to the Dilatino equation appearing in the Strominger system (a proposed notion of canonical metric structures outside the Kähler scenario). The talk is based on joint work with Federico Giusti.