Understandably, the focus of processing mapping methods is the activity. Healthy verb-noun structure (doing something to something) provides a good impression of what is going on. The activity boxes are then connected by single arrows, which in most cases simply indicate the direction of flow, but are generally unlabelled.
As processes have become increasingly completed, and the drive for productivity has resulted in more batch t, we need to use this inter-activity information more intelligently. This is compounded as we move from mapping simple linear processes and start to see activity networks emerging.
So what do we label these arrows as? My suggestion is to look for a noun that is recognised by the sending activity whose output it represents, and the receiving activity for whom it is an input. It is likely that we need to include some status information, as it is likely that a simple noun will appear between multiple activities. It may also be necessary to indicate the channel, or system via which the object is transmitted.
Its time we make the space between activities play its part in providing clarity.