Multiview video supports observing a scene from different viewpoints. The Joint Video Team (JVT) developed H.264/MVC to enhance the compression efficiency for multiview video, however, MVC encoded multiview video (MVC video) still requires high bitrates for transmission. This paper investigates live MVC video streaming over Peer-to-Peer (P2P) networks. The goal is to minimize the server bandwidth costs whist ensuring high streaming quality to peers. MVC employs intra-view and inter-view prediction structures, which leads to a complicated layer dependency relationship. As the peers' outbound bandwidth is shared while supplying all the MVC video layers, the bandwidth allocation to one MVC layer affects the available outbound bandwidth of the other layers. To optimise the utilisation of the peers' outbound bandwidth for providing video layers, a maximum flow based model is proposed which considers the MVC video layer dependency and the layer supplying relationship between peers. Based on the model, a layer dependency aware live MVC video streaming method over a BitTorrent-like P2P network is proposed, named MVP2P. The key components of MVP2P include a chunk scheduling strategy and a peer selection strategy for receiving peers, and a bandwidth scheduling algorithm for supplying peers. To evaluate the efficiency of the proposed solution, MVP2P is compared with existing methods considering the constraints of peer bandwidth, peer numbers, view switching rates, and peer churns. The test results show that MVP2P significantly outperforms the existing methods.