In this paper, we address the skyrmion-bimeron dynamical transformation during the propagation of such structures along a magnetic nanotrack with anisotropy gradients. Using a micromagnetic approach and simulations, we observe that a skyrmion continuously transforms into a bimeron, and vice versa (in a reversible way). Furthermore, our results show that the topological charge and the velocity of the intermediary magnetic textures emerging during the transformation are constant. These results can contribute to understanding the dynamic transformation between solitonic magnetic textures with the same topological charge.