The Big Data era requires new processing architectures, among which streaming systems which have become very popular. Those systems are able to summarize infinite data streams with aggregates on the most recent data. However, up to now, only point events have been considered and spanning events, which come with a duration, have been let aside, restricted to the persistent databases world only. In this paper, we propose a unified framework to deal with such stream mechanisms on spanning events. To this end, we formally define a spanning event stream with new stream semantics and events properties, particularly considering how the event is received. We then review and extend usual stream windows to meet the new spanning event requirements. Eventually, we validate the soundness of our new framework with a set of experiments, based on a straightforward implementation, showing that aggregation of spanning event stream is providing as much new insight on the data as effectiveness in several use cases.