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Most existing methods for category-level pose estimation rely on object point clouds. However, when considering transparent objects, depth cameras are usually not able to capture meaningful data, resulting in point clouds with severe artifacts. Without a high-quality point cloud, existing methods are not applicable to challenging transparent objects. To tackle this problem, we present StereoPose, a novel stereo image framework for category-level object pose estimation, ideally suited for transparent objects. For a robust estimation from pure stereo images, we develop a pipeline that decouples category-level pose estimation into object size estimation, initial pose estimation, and pose refinement. StereoPose then estimates object pose based on representation in the normalized object coordinate space~(NOCS). To address the issue of image content aliasing, we further define a back-view NOCS map for the transparent object. The back-view NOCS aims to reduce the network learning ambiguity caused by content aliasing, and leverage informative cues on the back of the transparent object for more accurate pose estimation. To further improve the performance of the stereo framework, StereoPose is equipped with a parallax attention module for stereo feature fusion and an epipolar loss for improving the stereo-view consistency of network predictions. Extensive experiments on the public TOD dataset demonstrate the superiority of the proposed StereoPose framework for category-level 6D transparent object pose estimation.