"successive stages" means different steps or phases that occur one after another in a series. It refers to a process where you go through a series of steps, with each step building or leading to the next step. Full definition
The key is two cultures of bacteria which provide «food» for one another in successive stages of the process. (newscientist.com)
This explains the supersession in successive stages of arthropods by vertebrates, of pisciforms by tetrapods, and finally, within the tetrapod group, the progressive predominance of the mammals, gradually forming their own primate strain, with the growth, globally irreversible and constantly accelerated along certain favored lines, of «cerebration» from the beginning of life up to the present time. (religion-online.org)
It is based on the definitive books of mouse embryonic development by Theiler (1989) and Kaufman (1992) yet extends these studies by creating a series of three dimensional computer models of mouse embryos at successive stages of development with defined anatomical domains linked by a stage - by - stage ontology of anatomical names. (discovery.lifemapsc.com)