Twitter new event detection aims to identify first stories in a tweet stream. Typical approaches consider two sub tasks. First, it is necessary to filter out mundane or irrelevant tweets. Second, tweets are grouped automatically into event clusters. Traditionally, these two sub tasks are processed separately, and integrated under a pipeline setting, despite that there is inter-dependence between the two tasks. In addition, one further related task is summarization, which is to extract a succinct summary for representing a large group of tweets. Summarization is related to detection, under the new event setting in that salient information is universal between event representing tweets and informative event summaries. In this paper, we build a joint model to filter, cluster, and summarize the tweets for new events. In particular, deep representation learning is used to vectorize tweets, which serves as basis that connects tasks. A neural stacking model is used for integrating a pipeline of different sub tasks, and for better sharing between the predecessor and successors. Experiments show that our proposed neural joint model is more effective compared to its pipeline baseline.