In the SSA22 field which exhibits a large-scale proto-cluster at $z=3.1$, we carried out a spectroscopic survey for Lyman Break Galaxies (LBGs) with the VLT/VIMOS and identified 78 confident LBGs at $z=2.5$--4. We stacked their spectra in the observers frame by using a sophisticated method. Analyzing the composite spectrum, we have revealed that the large-scale proto-cluster at $z=3.1$ has a strong HI absorption dip of rest-frame equivalent width of $-1.7$ A. Another strong absorption dip found at $z=3.28$ is associated with a modestly high-density LBG peak, similar to that at $z=3.1$. We have also detected an HI transparency peak at $z=2.98$ in the composite spectrum, coincident with a void in the LBG distribution. In this paper, we also investigated the relation between LBGs, HI gas and AGNs at $z=3$--4 in the SSA22 field. Two AGNs at $z=3.353$ and 3.801 are, respectively, associated with the LBG concentration of an overdensity factor $delta_{rm LBG}simeq2$ in the present statistics. Another structure at $z=3.453$ is remarkable: 20 comoving Mpc scale dense HI gas which is not associated with any apparent LBG overdensity but involving a pair of AGNs. Such structure may be a new type of the AGN-matter correlation. If the inhomogeneous structures over a comoving Gpc scale found in this paper are confirmed with sufficient statistics in the future, the SSA22 field will become a key region to test the standard cold dark matter structure formation scenario.
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