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On 13 May 1998, the Extreme-Ultraviolet Imaging Telescope (EIT, on board SOHO) has produced a unique image sequence operating in 'shutterless mode' (SOHO JOP 80). In JOP 80, EIT is the lead instrument, followed by several space-born instruments (SXT, TRACE, MDI, CDS, SUMER), as well as two observatories on the ground (in La Palma and Sac Peak). The target of the campaign was a relatively small but rapidly evolving active region (AR 8218). For the EIT contribution, a 15 s cadence was achieved in the Fe xii bandpass at 195 A by leaving EIT's shutter open for 1 h and operating the CCD in frame-transfer mode. In this paper, we start the analysis of the huge data set, by making an inventory of the transients observed in the EIT image sequence. Besides scatter plots of duration, size and radiative output of the detected EUV brightenings, we discuss in full detail the morphology and evolution of several typical events. These transients range from a B3.5 flare producing a large plasma flow along pre-existing loops, to EUV versions of active region transient brightenings as previously observed by SXT on board Yohkoh. In addition, a new class of weaker footpoint brightenings is discussed that produce wave-like disturbances propagating along quasi-open field lines. This new class of propagating disturbances extends the wide variety of transient phenomena that we discovered in the EIT data, and makes the potential for inter-instrumental studies of the JOP 80 data all the more exciting. We stress the necessity of such forthcoming studies to reach an instrument-independent classification of small-scale solar transients.