  Two outbursts were observed by RXTE in the history of the atoll source IGR
J17473-2721. During the most recent outburst in 2008, the source showed a
complete series of spectral states/transitions. The neutron star system was
prolific in type-I X-ray bursts, and we investigate them in the context of
complete outbursts evolution. A total exposure of ~ 309 ks was collected by
RXTE during the two outbursts of IGR J17473-2721. We carried out a systematic
search for type-I bursts in this data set. For each burst found, we
investigated the burst profile, the peak flux, and their dependence on the
accretion rate along the evolution of the outbursts. Eighteen type-I X-ray
bursts were found from IGR J17473-2721: two from the outburst in 2005 and the
other 16 from the recent outburst in 2008. Among them, 3 bursts show
photospheric radius expansion (PRE). The distance to the source is estimated as
6.4 kpc with a 15% uncertainty based on the three bursts that show PRE. In the
recent outburst, there are 6 bursts showing up in the low/hard state prior to
the state transition to a high/soft state, 3 bursts at the end phase of the
high/soft state, and 7 in the following low/hard state. The blackbody radius of
these bursts presents a variety of interesting features. We find that at the
end of the recent outburst, the profile of the blackbody radius is
anti-correlated with the blackbody temperature and the burst flux. The
durations of the type-I burst are found to correlate with the Eddington ratio
and to have two parallel evolution groups. Along the decreasing Eddington
ratio, the burst duration decreases and ends in each group the PRE bursts
occurred. This provides new clues to the type-I bursts in the context of
outbursts for atoll XRBs.
