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We searched for thermonuclear X-ray bursts from Galactic neutron stars in allevent mode data of the Neil Gehrels Swift Observatory collected until March 31,2018. In particular, we are interested in the intermediate-duration bursts(shell flashes fueled by thick helium piles) with the ill-understood phenomenonof strong flux fluctuations. Nine such bursts have been discussed in theliterature to date. Swift is particularly suitable for finding additionalexamples. We find and list a total of 134 X-ray bursts; 44 are detected withBAT only, 41 with XRT only, and 49 with both. Twenty-eight bursts involveautomatic slews. We find 12 intermediate-duration bursts, all detected inobservations involving automatic slews. Five show remarkably longEddington-limited phases in excess of 200 s. Five show fluctuations during thedecay phase; four of which are first discussed in the present study. We discussthe general properties of the fluctuations, considering also 7 literaturecases. In general two types of fluctuations are observed: fast ones, with atypical timescale of 1 s and up and downward fluctuations of up to 70%, andslow ones, with a typical timescale of 1 min and only downward fluctuations ofup to 90%. The latter look like partial eclipses because the burst decayremains visible in the residual emission. We revisit the interpretation of thisphenomenon in the context of the new data set and find that it has not changedfundamentally despite the expanded data set. It is thought to be due to adisturbance of the accretion disk by outflowing matter and photons, causingobscuration and reflection due to Thompson scattering in an orbiting highlyionized cloud or structure above or below the disk. We discuss in detail themost pronounced burster SAX J1712.6-3739. One of the bursts from this source isunusual in that it lasts longer than 5600 s, but does not appear to be asuperburst.

Searching for the most powerful thermonuclear X-ray bursts with the Neil Gehrels Swift Observatory