Most existing training systems focus on a single region. In contrast, we envision that cross-region training offers more flexible GPU resource allocation and yields significant potential. However, the hierarchical cluster topology and unstable networks in the cloud-edge-end (CEE) environment, a typical cross-region scenario, pose substantial challenges to building an efficient and autonomous model training system. We propose DeepCEE, a geo-distributed model training system tailored for heterogeneous GPUs and networks in CEE environments. DeepCEE adopts a communication-centric design philosophy to tackle challenges arising from slow and unstable inter-region networks. It begins with a heterogeneous device profiler that identifies and groups devices based on both network and compute characteristics. Leveraging device groups, DeepCEE implements compact, zero-bubble pipeline parallelism, automatically deriving optimal parallel strategies. To further adapt to runtime variability, DeepCEE integrates a dynamic environment adapter that reacts to network fluctuations. Extensive evaluations demonstrate that DeepCEE achieves 1.3-2.8x higher training throughput compared to widely used and SOTA training systems.