Relative excesses of redshift number densities compared to the field expectation, as a function of rest-frame velocity window (Δv; left-hand panels) and maximum impact parameter to the closest cluster-pair axis (Δd; right-hand panels), for fixed Δd = 3 Mpc and Δv = 1000 km s⁻¹ values respectively. The top panels show those for total H i (brown circles, solid lines) and O vi (green squares, dashed lines) absorption line samples. The bottom panels show those for narrow (NLA; b < 50 km s⁻¹; blue triangles, solid lines) and broad (BLAs; b ≥ 50 km s⁻¹; red pentagons, dashed lines) H i absorption line samples. Coloured light shaded areas represent ±1σ statistical uncertainties. See Section 6.2 for further details.