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Cooperative Intelligent Transportation Systems (C-ITS) will change the modes of road safety and traffic management, especially at intersections without traffic lights, namely unsignalized intersections. Existing researches focus on vehicle control within a small area around an unsignalized intersection. In this paper, we expand the control domain to a large area with multiple intersections. In particular, we propose a Multi-intersection Vehicular Cooperative Control (MiVeCC) to enable cooperation among vehicles in a large area with multiple unsignalized intersections. Firstly, a vehicular end-edge-cloud computing framework is proposed to facilitate end-edge-cloud vertical cooperation and horizontal cooperation among vehicles. Then, the vehicular cooperative control problems in the cloud and edge layers are formulated as Markov Decision Process (MDP) and solved by two-stage reinforcement learning. Furthermore, to deal with high-density traffic, vehicle selection methods are proposed to reduce the state space and accelerate algorithm convergence without performance degradation. A multi-intersection simulation platform is developed to evaluate the proposed scheme. Simulation results show that the proposed MiVeCC can improve travel efficiency at multiple intersections by up to 4.59 times without collision compared with existing methods.