The simplest cuprate superconductor La2CuO4+y with mobile oxygen interstitials exhibits a clear phase separation. It is known that oxygen interstitials enter into the rocksalt La2O2+y spacer layers forming oxygen interstitials rich puddles and poor puddles but only recently a bulk multiscale structural phase separation has been observed by using scanning micro X-ray diffraction. Here we get further information on their spatial distribution, using scanning La L-3-edge micro X-ray absorption near edge structure. Percolating networks of oxygen rich puddles are observed in different micrometer size portions of the crystals. Moreover, the complex surface resistivity shows two jumps associated to the onset of intra-puddle and inter-puddles percolative superconductivity. The similarity of oxygen doped La2CuO4+y, with the well established phase separation in iron selenide superconductors is also discussed. (C) 2014 AIP Publishing LLC.