Open skies, as usually defined, grants all carriers of the two countries unlimited fourth-freedom rights (the right to fly from their own country to another). It is a separate issue from fifth-freedom rights, which allow a carrier to fly between two countries neither of which is its own. (There's a whole list. IIRC, first freedom is overflight, second is stopping for repairs, third is taking on cargo, etc... cabotage would be 8th freedom.)