It is perfectly safe to run the pool pump while the solar cover is on the pool. The solar cover does not interfere with the water circulation of the pump at all and does not get sucked into the skimmer. By running the pump with the solar cover on, you can save time and money on pool maintenance.
Solar Pool Covers also keep debris and dirt out of the pool. The solar cover helps to eliminate debris and algae spores getting into the water. This effectively keeps your pool cleaner for longer and reduces the amount of maintenance needed.
With the pool pump running, the warmer water under the solar cover will be able to mix with the colder water at the bottom of the pool, thus creating an even water temperature throughout the pool.