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Federated learning (FL) over resource-constrained wireless networks has recently attracted much attention. However, most existing studies consider one FL task in single-cell wireless networks and ignore the impact of downlink/uplink inter-cell interference on the learning performance. In this paper, we investigate FL over a multi-cell wireless network, where each cell performs a different FL task and over-the-air computation (AirComp) is adopted to enable fast uplink gradient aggregation. We conduct convergence analysis of AirComp-assisted FL systems, taking into account the inter-cell interference in both the downlink and uplink model/gradient transmissions, which reveals that the distorted model/gradient exchanges induce a gap to hinder the convergence of FL. We characterize the Pareto boundary of the error-induced gap region to quantify the learning performance trade-off among different FL tasks, based on which we formulate an optimization problem to minimize the sum of error-induced gaps in all cells. To tackle the coupling between the downlink and uplink transmissions as well as the coupling among multiple cells, we propose a cooperative multi-cell FL optimization framework to achieve efficient interference management for downlink and uplink transmission design. Results demonstrate that our proposed algorithm achieves much better average learning performance over multiple cells than non-cooperative baseline schemes.