Generating vivid and emotional 3D co-speech gestures is crucial for virtual avatar animation in human-machine interaction applications. While the existing methods enable generating the gestures to follow a single emotion label, they overlook that long gesture sequence modeling with emotion transition is more practical in real scenes. In addition, the lack of large-scale available datasets with emotional transition speech and corresponding 3D human gestures also limits the addressing of this task. To fulfill this goal, we first incorporate the ChatGPT-4 and an audio inpainting approach to construct the high-fidelity emotion transition human speeches. Considering obtaining the realistic 3D pose annotations corresponding to the dynamically inpainted emotion transition audio is extremely difficult, we propose a novel weakly supervised training strategy to encourage authority gesture transitions. Specifically, to enhance the coordination of transition gestures w.r.t. different emotional ones, we model the temporal association representation between two different emotional gesture sequences as style guidance and infuse it into the transition generation. We further devise an emotion mixture mechanism that provides weak supervision based on a learnable mixed emotion label for transition gestures. Last, we present a keyframe sampler to supply effective initial posture cues in long sequences, enabling us to generate diverse gestures. Extensive experiments demonstrate that our method outperforms the state-of-the-art models constructed by adapting single emotion-conditioned counterparts on our newly defined emotion transition task and datasets.