Evolution of a Buddha vs. Anatta

Based on the lifestory of Shakyamuni Buddha, one can see that there is an evolution, from disciple to boddhisatva until the Buddhahood stage... like a path his mind was following, but we know minds just go around samsara up and down, nothing except seeds of kamma goes along with the mind, no such thing as a soul. So how can one relate that to Anatta?