We explore the structure of singularities for Calabi-Yau elliptic fibrations by studying the crepant resolutions of such spaces. The resolutions are obtained by considering the phase structure of the Coulomb branch of the gauge theory arising from the M-theory compactification on the Calabi-Yau. One finds that associated to fibral singularities located above codimension two in the base of the fibration is a representation of the group that is associated to the singularities above codimension one. The set of distinct crepant resolutions is then the possible choices of a certain decoration on this representation, and the relations between these decorations express, via flop transitions, the relations among the distinct resolved geometries.