Hello Erich.
The Royal Air Force were in complete control of the air space over Normandy, I have heard somewhere, that the number of British fighter planes available were 7000. The German Air Force was only to be seen on quick forays, and then away. The Naval gunfire was provided by the British Navy and was devastating in its effect.
The greatest use of Air Power for supporting the Soldiers that did the fighting, was the "Typhoon" a British rocket firing fighter. As the campaign developed we had a "Cab Rank" of Typhoons flying over the battle areas, available to take out "dug in tanks" (hull down) or heavily defended positions. To explain Taxi cabs are parked in what is known as "Cab ranks" Typhoons served the purpose of being available from the 'taxi park' therefore the "cab rank" of "Tiffy's"

These 'Typhoons seemed to stand still momentarily in the air when they fired their rockets. Some of the British Fighters complained, that as they ranged widely across the face of France, they had run out of targets!.
Hope this is answers your question.
Sapper.