Deleterious mutations accumulating on non-recombining Y chromosomes can drive XY to XY turnovers, as they allow to replace the old mutation-loaded Y by a new mutation-free one. The same process is thought to prevent XY to ZW turnovers, because the latter requires fixation of the ancestral Y, assuming dominance of the emergent feminizing mutation. Using individual-based simulations, we explored whether and how an epistatically dominant W allele can spread in a young XY system that gradually accumulates deleterious mutations. We also investigated how sexually antagonistic (SA) polymorphism on the ancestral sex chromosomes and the mechanism controlling X-Y recombination suppression affect these transitions. In contrast with XY to XY turnovers, XY to ZW turnovers cannot be favored by Y chromosome mutation load. If the arrest of X-Y recombination depends on genotypic sex, transitions are strongly hindered by deleterious mutations, and totally suppressed by very small SA cost, because deleterious mutations and female-detrimental SA alleles would have to fix with the Y. If, however, the arrest of X-Y recombination depends on phenotypic sex, X and Y recombine in XY ZW females, allowing for the purge of Y-linked deleterious mutations and loss of the SA polymorphism, causing XY to ZW turnovers to occur at the same rate as in the absence of deleterious and sex-antagonistic mutations. We generalize our results to other types of turnovers (e.g., triggered by non-dominant sex-determining mutations) and discuss their empirical relevance.