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We present a complete and homogeneous analysis of the Ly$α$ emission properties of the cosmic web at $3 \lesssim z \lesssim 5$ as a function of the overdensity of Ly$α$ emitters (LAEs) in the MUSE Ultra Deep Field (MUDF) and the MUSE Extremely Deep Field (MXDF).
Acknowledgement WL thanks John Silverman for his constructive suggestions. W.L. acknowledges support from NASA through STScI grants JWST-Survey-3428 and HST-GO-17758. R.D. acknowledges support from the PRORIS 2025 “CosmoWebb” and the INAF minigrant 2024: “The interstellar medium at high redshift.” M.O. is supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI grant No. 24K22894 and 26K07155.
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