  We present MUSE observations of the gas-rich major-merger BR1202-0725 at
z~4.7, which constitutes one of the most overdense fields known in the early
Universe. We utilise these data in conjunction with existing ALMA observations
to compare and contrast the spatially resolved ionised- and cool-gas content of
this system which hosts a quasar (QSO), a sub-millimeter galaxy (SMG), the two
known optical companions ("LAE1", "LAE2"), and an additional companion
discovered in this work "LAE3" just 5 arcsec to the North of the QSO. We find
that QSO BR1202-0725 exhibits a large Ly$\alpha$ halo, covering $\approx55$
pkpc on-sky at surface brightness levels of SB$\geq$1E-17
erg/s/cm$^2$/arcsec$^2$. In contrast, the SMG, of similar far-infrared
luminosity and star formation rate (SFR), does not exhibit such a Ly$\alpha$
halo. The QSO's halo exhibits high velocity widths ($\sim1000$ km/s) but the
gas motion is to some extent kinematically coupled with the previously observed
[CII] bridge between the QSO and the SMG. We note that the object known in the
literature as LAE2 shows no local peak of Ly$\alpha$ emission, rather, its
profile is more consistent with being part of the QSO's extended Ly$\alpha$
halo. The properties of LAE3 are typical of high-redshift LAEs; we measure
F$_{\rm{Ly\alpha}}$(LAE3) = $0.24\pm$0.03E-16 erg/s/cm$^2$, corresponding to
SFR$_{\rm{Ly\alpha}}\approx\ $5.0$\pm$0.5 M${_\odot}$/yr. The velocity width is
$\Delta v$(LAE3) $\approx 400$ km/s, and equivalent width
EW$_0$(Ly$\alpha_{\,5\sigma}^{\,lim})\geq 34.05$ $\\A$, consistent with star
formation being the primary driver of Ly$\alpha$ emission. We also note a
coherent absorption feature at $\sim -400$km/s in spectra from at least three
objects; the QSO, LAE1 and "LAE2" which could imply the presence of an
expanding neutral gas shell with an extent of at least $24$ pkpc.
