For a smooth minimally elliptic surfaces, all the possible singular fibres that can occur were classified by Kodaira.

In the case of threefolds, its classification gives only some of the possible singular fibres: in fact it works only for the generic singular fibre. Over some point on the base of the fibration, in fact, we may have non-Kodaira fibres.

In this talk, we want to deal with the problem of classifying the singular fibres of non-Kodaira type in a smooth elliptic threefold, and in particular to focus on their relationship with the Kodaira fibres.

We will focus on the class of smooth elliptic threefolds which looks closer to the one of smooth minimally elliptic surfaces with respect to the Weierstrass model, namely the one of smooth equidimensional elliptic threefolds for which the morphism to the Weierstrass model is a crepant resolution, and we will show that for such fibrations the possible singular fibres of non-Kodaira type are obtained as the contraction of some Kodaira fibre.