Deforming Namikawa's fiber products

The aim of the present paper is giving a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y.~Namikawa in Remark 2.8 and Example 1.11 of Namikawa (2002). Moreover an application in the context of deformations of small geometric transitions to conifold transitions is described.