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We report the discovery of three double-peaked Lyman-$\alpha$ emitters (LAEs)exhibiting strong blue peak emission at 2.9 $\lesssim z \lesssim$ 4.8, in theVLT/MUSE data obtained as part of the Middle Ages Galaxy Properties withIntegral Field Spectroscopy (MAGPI) survey. These strong blue peak systemsprovide a unique window into the scattering of Lyman-$\alpha$ photons byneutral hydrogen (HI), suggesting gas inflows along the line-of-sight and lowHI column density. Two of them at $z=2.9$ and $z=3.6$ are spatially extendedhalos with their core regions clearly exhibiting stronger blue peak emissionsthan the red peak. However, spatial variations in the peak ratio and peakseparation are evident over $25\times 26$ kpc ($z=2.9$) and $19\times28$ kpc($z=3.6$) regions in these extended halos. Notably, these systems do not fallin the regime of Lyman-$\alpha$ blobs or nebulae. To the best of our knowledge,such a Lyman-$\alpha$ halo with a dominant blue core has not been observedpreviously. In contrast, the LAE at $z\sim4.8$ is a compact system spanning a$9\times9$ kpc region and stands as the highest-redshift strong blue peakemitter ever detected. The peak separation of the bright cores in these threesystems ranges from $\Delta_{\mathrm{peak}}\sim370$ to $660$ km/s. The observedoverall trend of decreasing peak separation with increasing radius is supposedto be controlled by HI column density and gas covering fraction. Based onvarious estimations, in contrast to the compact LAE, our halos are found to begood candidates for LyC leakers. These findings shed light on the complexinterplay between Lyman-$\alpha$ emission, gas kinematics, and ionisingradiation properties, offering valuable insights into the evolution and natureof high-redshift galaxies.

Compact to extended Lyman-$\alpha$ emitters in MAGPI: strong blue peak emission at $z\gtrsim3$