Redshifts of local galaxies are examined for quantization and variability after transformation to the cosmic background rest frame. Ordinary spiral galaxies with 21 cm profile widths near 200 km s-1 show periodic redshifts, and what appears to be variability between levels, at a predicted period near 18.3 km s-1 and its higher harmonics. Evidence for variability is based on several independent sets of data. The asymmetry of 21 cm profiles seems to be related to the ordering of galaxies within transition sequences between quantized redshift levels.Galaxies near 200 km s-1 in profile width appear to populate a transition region in quantization properties. As wider profile spirals are examined, the 18.3 km s-1 periodicity is replaced by a 5.76 km s-1 periodicity belonging to a different family of predicted periods. A similar transition in properties occurs at the boundary between common spirals and dwarf galaxies with intermediate width 21 cm profiles. The ordinary dwarf galaxies show a 46.1 km s-1 period belonging to the same family of predicted periods found for wide profile spirals. The periods involved in the study are predicted by the three-dimensional time model described by Tifft in 1996. Certain families and ranges of periods are preferred. It appears that galaxies can be divided into several distinct classes within which we find both similar morphological and quantization properties. A discussion of binomial statistical testing of period fits is given in an appendix.