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We study the geometric engineering of gauge theories with gauge group Spin(4)and SO(4) using crepant resolutions of Weierstrass models. The correspondingelliptic fibrations realize a collision of singularities corresponding to twofibers with dual graph the affine $A_1$ Dynkin diagram. There are eightdifferent ways to engineer such collisions using decorated Kodaira fibers. TheMordell-Weil group of the elliptic fibration is required to be trivial forSpin(4) and Z/2Z for SO(4).  Each of these models have two possible crepant resolutions connected by aflop. We also compute a generating function for the Euler characteristic ofsuch elliptic fibrations over a base of arbitrary dimensions. In the case of athreefold, we also compute the triple intersection numbers of the fibraldivisors. In the case of Calabi-Yau threefolds, we also compute their Hodgenumbers, and check the cancellations of anomalies in a six-dimensionalsupergravity theory.

Flopping and Slicing: SO(4) and Spin(4)-models