Video depth estimation is crucial in various applications, such as scene reconstruction and augmented reality. In contrast to the naive method of estimating depths from images, a more sophisticated approach uses temporal information, thereby eliminating flickering and geometrical inconsistencies. We propose a consistent method for dense video depth estimation; however, unlike the existing monocular methods, ours relates to stereo videos. This technique overcomes the limitations arising from the monocular input. As a benefit of using stereo inputs, a left-right consistency loss is introduced to improve the performance. Besides, we use SLAM-based camera pose estimation in the process. To address the problem of depth blurriness during test-time training (TTT), we present an edge-preserving loss function that improves the visibility of fine details while preserving geometrical consistency. We show that our edge-aware stereo video model can accurately estimate the dense depth maps.