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In this paper, we consider the cooperative spectrum sensing problem for a cognitive radio (CR) mesh network, where secondary users (SUs) are allowed to share the spectrum band which is originally allocated to a primary users' (PUs) network. We propose two new cooperative spectrum sensing strategies, called amplify-and-relay (AR) and detect-and-relay (DR), aiming at improving the detection performance with the help of other eligible SUs so as to agilely vacate the channel to the primary network when the neighboring PUs switch to active state. AR and DR strategies are periodically executed during the spectrum sensing phase which is arranged at the beginning of each MAC frame. Based on AR and DR strategies, we derive the closed-form expressions of false alarm probability and detection probability for both single-relay and multi-relay models, with or without channel state information (CSI). Simulation results show that our proposed strategies achieve better performance than a non-cooperative (or non-relay) spectrum sensing method and an existing cooperative detection method. As expected, we observe that the detection performance improves as the number of eligible relay SUs increases, and furthermore, it is better for the known-CSI case than that of the unknown-CSI case.