The neutron star low-mass X-ray binary GRS 1741.9-2853 is a known type-I burster of the Galactic Center. It is transient, faint, and located in a very crowded region, only 10 arcmin from the supermassive black hole Sgr A*. Therefore, its bursting behavior has been poorly studied so far. In particular, its persistent emission has rarely been detected between consecutive bursts, due to lack of sensitivity or confusion. This is what made GRS 1741.9-2853 one of the nine burst-only sources identified by BeppoSAX a few years ago. The physical properties of GRS 1741.9-2853 bursts are yet of great interest since we know very little about the nuclear regimes at stake in low accretion rate bursters. We examine here for the first time several bursts in relation with the persistent emission of the source, using INTEGRAL, XMM-Newton, and Swift observations. We investigate the source flux variability and bursting behavior during its 2005 and 2007 long outbursts. The persistent luminosity of GRS 1741.9-2853 varied between ~1.7 and 10.5 10^36 erg s^-1, i.e. 0.9-5.3% of the Eddington luminosity. The shape of the spectrum as described by an absorbed power-law remained with a photon index Gamma ~ 2 and a column density $N_{rm H} ~ 12 10^22 cm^-2 throughout the outbursts. We discovered 11 type-I bursts with INTEGRAL, and inspected 4 additional bursts: 2 recorded by XMM-Newton and 2 by Swift. From the brigthest burst, we derive an upper limit on the source distance of ~7 kpc. The observed bursts characteristics and source accretion rate suggest pure helium explosions igniting at column depths y_{ign} ~ 0.8-4.8 10^8 g cm^-1, for typical energy releases of ~1.2-7.4 10^39 erg.
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