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Learning urban region embeddings has substantially advanced urban analysis, but their typical focus on individual cities leads to disparate embedding spaces, hindering cross-city knowledge transfer and the reuse of downstream task predictors. To tackle this issue, we present Consistent Region Embedding (CoRE), a unified framework integrating region embedding learning with cross-city latent space alignment. CoRE first embeds regions from two cities into separate latent spaces, followed by the alignment of latent space manifolds and fine-grained individual regions from both cities. This ensures compatible and comparable embeddings within aligned latent spaces, enabling predictions of various socioeconomic indicators without ground truth labels by migrating knowledge from label-rich cities. Extensive experiments show CoRE outperforms competitive baselines, confirming its effectiveness for cross-city knowledge transfer via aligned latent spaces.