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In the current demand for automation in the agro-food industry, accurately detecting and localizing relevant objects in 3D is essential for successful robotic operations. However, this is a challenge due the presence of occlusions. Multi-view perception approaches allow robots to overcome occlusions, but a tracking component is needed to associate the objects detected by the robot over multiple viewpoints. Most multi-object tracking (MOT) algorithms are designed for high frame rate sequences and struggle with the occlusions generated by robots' motions and 3D environments. In this paper, we introduce MOT-DETR, a novel approach to detect and track objects in 3D over time using a combination of convolutional networks and transformers. Our method processes 2D and 3D data, and employs a transformer architecture to perform data fusion. We show that MOT-DETR outperforms state-of-the-art multi-object tracking methods. Furthermore, we prove that MOT-DETR can leverage 3D data to deal with long-term occlusions and large frame-to-frame distances better than state-of-the-art methods. Finally, we show how our method is resilient to camera pose noise that can affect the accuracy of point clouds. The implementation of MOT-DETR can be found here: https://github.com/drapado/mot-detr