The explosion mechanism associated with thermonuclear supernovae (SNIa) is still a matter of debate. Nevertheless, there is a wide agreement that high amounts of radioactive nuclei are produced during these events, that are expected to be strong γ-ray emitters. In this paper we investigate the use of γ-rays as a diagnostic tool. For this purpose we have performed a complete study of the γ-ray spectra associated with all the different scenarios currently proposed: detonation, deflagration, delayed detonation, pulsating delayed detonation and off-center detonation. Our study shows that the γ-ray emission from SNIa is, effectively, a promising tool but that must be carefully used since it can lead to misinterpretations. We also show that 3D effects might be relevant in some circumstances and provide important information about the exploding system and the thermonuclear burning front mechanism if high resolution spectra are obtained.

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