We present an analysis of the relative frequencies of different supernova (SN) types in spirals with various morphologies and in barred or unbarred galaxies. We use a well-defined and homogeneous sample of spiral host galaxies of 692 SNe from the Sloan Digital Sky Survey in different stages of galaxy-galaxy interaction and activity classes of nucleus. We propose that the underlying mechanisms shaping the number ratios of SNe types can be interpreted within the framework of interaction-induced star formation, in addition to the known relations between morphologies and stellar populations. We find a strong trend in behaviour of the N_Ia_/N_CC_ ratio depending on host morphology, such that early spirals include more Type Ia SNe. The N_Ibc_/N_II_ ratio is higher in a broad bin of early-type hosts. The N_Ia_/N_CC_ ratio is nearly constant when changing from normal, perturbed to interacting galaxies, then declines in merging galaxies, whereas it jumps to the highest value in post-merging/remnant galaxies. In contrast, the N_Ibc_/N_II_ ratio jumps to the highest value in merging galaxies and slightly declines in post-merging/remnant subsample. The interpretation is that the star formation rates and morphologies of galaxies, which are strongly affected in the final stages of interaction, have an impact on the number ratios of SNe types. The N_Ia_/N_CC_ (N_Ibc_/N_II_) ratio increases (decreases) from star-forming to active galactic nuclei (AGN) classes of galaxies. These variations are consistent with the scenario of an interaction-triggered starburst evolving into AGN during the later stages of interaction, accompanied with the change of star formation and transformation of the galaxy morphology into an earlier type.