When students first learn solid state physics the concept of holes and its utility is not easy to grasp. I find it really helpful to use the Solid state simulations program ziman very helpful to illustrate the difference between electrons and holes.
One can consider the motion of electrons in Bloch states for a band structure with the energy contours shown in green in the figure below. One can vary the external magnetic and electric field.
If one goes to preset 6 (which has zero electric field) one can start an electron on an electron or a hole Fermi surface. One sees that the motion in a magnetic field has the opposite circulation for electrons and holes, in both real and Bloch wave vector space.
Hence, the holes really do act like positively charged particles.