Two rubber balloons: Phase diagram of air transfer

Two identical rubber balloons are partially inflated with air (to different extent) and connected by a hose with a valve. It is found that depending on initial balloon volumes, when the valve is opened the air will flow either from the larger (fuller) balloon to the smaller (emptier) balloon, or from the smaller balloon to the larger one. The phenomenon is explained in terms of the nonideal rubber elasticity of balloons. The full phase diagram for the air flow dynamics is constructed.