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We explore the benefit of feedback for physical layer interference management in wireless networks without centralized upper layer control mechanisms. Lack of coordination in the upper layer could make the interference experienced in the physical layer bursty. To understand how to harness such burstiness with feedback, we investigate a two-user bursty interference channel (IC), where the presence of interference is governed by a Bernoulli random state. We completely characterize the capacity region of the symmetric two-user linear deterministic bursty IC with feedback. The proposed two-phase scheme exploits feedback either for refining the previous interfered reception or for relaying additional information to the legitimate receiver of the other user. Matching outer bounds are derived by novel techniques that take the effect of delayed state information into account. We also use insights from the deterministic case to characterize the approximate symmetric capacity for the symmetric Gaussian bursty IC with feedback in the weak interference regime.