Type Ia supernovae (SNe Ia) may originate from a wide variety of explosion scenarios and progenitor channels. They exhibit a factor of ≈10 difference in brightness and thus a differentiation in the mass of 56Ni → 56Co → 56Fe. We present a study on the fate of positrons within SNe Ia in order to evaluate their escape fractions and energy spectra. Our detailed Monte Carlo transport simulations for positrons and γ-rays include both β+ decay of 56Co and pair production. We simulate a wide variety of explosion scenarios, including the explosion of white dwarfs (WDs) close to the Chandrasekhar mass (MCh), He-triggered explosions of sub-MCh WDs, and dynamical mergers of two WDs. For each model, we study the influence of the size and morphology of ...