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Cosmological correlation functions contain valuable information about the primordial Universe, with possible signatures of new massive particles at very high energies. Recent developments, including the cosmological bootstrap, bring new perspectives and powerful tools to study these observables. In this paper, we systematically classify inflationary three-point correlators of scalar perturbations using the bootstrap method. For the first time, we derive a complete set of single-exchange cosmological collider bispectra with new shapes and potentially detectable signals. Specifically, we focus on the primordial scalar bispectra generated from the exchange of massive particles with all possible boost-breaking interactions during inflation. We introduce three-point "seed" functions, from which we bootstrap the inflationary bispectra of scalar and spinning exchanges using weight-shifting and spin-raising operators. The computation of the seed function requires solving an ordinary differential equation in comoving momenta, a boundary version of the equation of motion satisfied by a propagator that linearly mixes a massive particle with the external light scalars. The resulting correlators are presented in analytic form, for any kinematics. These shapes are of interest for near-future cosmological surveys, as the primordial non-Gaussianity in boost-breaking theories can be large. We also identify new features in these shapes, which are phenomenologically distinct from the de Sitter invariant cases. For example, the oscillatory shapes around the squeezed limit have different phases. Furthermore, when the massive particle has much lower speed of sound than the inflaton, oscillatory features appear around the equilateral configuration.