Open-domain conversational agents or chatbots are becoming increasingly popular in the natural language processing community. One of the challenges is enabling them to converse in an empathetic manner. Current neural response generation methods rely solely on end-to-end learning from large scale conversation data to generate dialogues. This approach can produce socially unacceptable responses due to the lack of large-scale quality data used to train the neural models. However, recent work has shown the promise of combining dialogue act/intent modelling and neural response generation. This hybrid method improves the response quality of chatbots and makes them more controllable and interpretable. A key element in dialog intent modelling is the development of a taxonomy. Inspired by this idea, we have manually labeled 500 response intents using a subset of a sizeable empathetic dialogue dataset (25K dialogues). Our goal is to produce a large-scale taxonomy for empathetic response intents. Furthermore, using lexical and machine learning methods, we automatically analysed both speaker and listener utterances of the entire dataset with identified response intents and 32 emotion categories. Finally, we use information visualization methods to summarize emotional dialogue exchange patterns and their temporal progression. These results reveal novel and important empathy patterns in human-human open-domain conversations and can serve as heuristics for hybrid approaches.