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In this paper, we evaluate the performance of an outage-optimal two-way opportunistic relaying (TWOR) scheme with analog network coding (ANC) over independent but not necessarily identically distributed (i.ni.d.) Nakagami-m fading channels. Considering arbitrary integer-valued fading parameters over the two hops, we derive an exact outage expression that is applicable for the entire range of signal-to-noise ratio (SNR). For better insights, we provide simple closed-form expressions at high SNR for bounds on the outage probability and on the ergodic sum-rate of the scheme. We show that the achievable diversity order is equal to the minimum of the per-hop fading parameters times the number of relaying candidates. Numerical and simulation results are presented to illustrate the theoretical analysis and the effects of the various Nakagami fading conditions on the overall system performance.