Traffic flow forecasting is a crucial task in urban computing. The challenge arises as traffic flows often exhibit intrinsic and latent spatio-temporal correlations that cannot be identified by extracting the spatial and temporal patterns of traffic data separately. We argue that such correlations are universal and play a pivotal role in traffic flow. We put forward {spacetime interval learning} as a paradigm to explicitly capture these correlations through a unified analysis of both spatial and temporal features. Unlike the state-of-the-art methods, which are restricted to a particular road network, we model the universal spatio-temporal correlations that are transferable from cities to cities. To this end, we propose a new spacetime interval learning framework that constructs a local-spacetime context of a traffic sensor comprising the data from its neighbors within close time points. Based on this idea, we introduce local spacetime neural network (STNN), which employs novel spacetime convolution and attention mechanism to learn the universal spatio-temporal correlations. The proposed STNN captures local traffic patterns, which does not depend on a specific network structure. As a result, a trained STNN model can be applied on any unseen traffic networks. We evaluate the proposed STNN on two public real-world traffic datasets and a simulated dataset on dynamic networks. The experiment results show that STNN not only improves prediction accuracy by 4% over state-of-the-art methods, but is also effective in handling the case when the traffic network undergoes dynamic changes as well as the superior generalization capability.