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Recent works on multi-modal emotion recognition move towards end-to-end models, which can extract the task-specific features supervised by the target task compared with the two-phase pipeline. However, previous methods only model the feature interactions between the textual and either acoustic and visual modalities, ignoring capturing the feature interactions between the acoustic and visual modalities. In this paper, we propose the multi-modal end-to-end transformer (ME2ET), which can effectively model the tri-modal features interaction among the textual, acoustic, and visual modalities at the low-level and high-level. At the low-level, we propose the progressive tri-modal attention, which can model the tri-modal feature interactions by adopting a two-pass strategy and can further leverage such interactions to significantly reduce the computation and memory complexity through reducing the input token length. At the high-level, we introduce the tri-modal feature fusion layer to explicitly aggregate the semantic representations of three modalities. The experimental results on the CMU-MOSEI and IEMOCAP datasets show that ME2ET achieves the state-of-the-art performance. The further in-depth analysis demonstrates the effectiveness, efficiency, and interpretability of the proposed progressive tri-modal attention, which can help our model to achieve better performance while significantly reducing the computation and memory cost. Our code will be publicly available.