Despite the impressive performance under the single-domain setup, current fully-supervised models for person re-identification (re-ID) degrade significantly when deployed to an unseen domain. According to the characteristics of cross-domain re-ID, such degradation is mainly attributed to the dramatic variation within the target domain and the severe shift between the source and target domain. To achieve a model that generalizes well to the target domain, it is desirable to take both issues into account. In terms of the former issue, one of the most successful solutions is to enforce consistency between nearest-neighbors in the embedding space. However, we find that the search of neighbors is highly biased due to the discrepancy across cameras. To this end, we improve the vanilla neighborhood invariance approach by imposing the constraint in a camera-aware manner. As for the latter issue, we propose a novel cross-domain mixup scheme. It alleviates the abrupt transfer by introducing the interpolation between the two domains as a transition state. Extensive experiments on three public benchmarks demonstrate the superiority of our method. Without any auxiliary data or models, it outperforms existing state-of-the-arts by a large margin. The code is available at https://github.com/LuckyDC/generalizing-reid.