The synthesis of the HgBa2CaCu2O6+δ (Hg-1212) superconductor under various experimental conditions in sealed silica tubes is reported. Optimization of synthesis conditions allowed the preparation of bulk superconducting Hg-1212 with Tc onset at 127 K and lattice parameters a=3.858 A ̊, c=12.68 A ̊. The neutron powder diffraction analysis yielded δ=0.22(4). As a result of different atmosphere annealings a relationship between the decrease of Tc and the increase of the lattice parameter a is deduced. A 300°C/10 h treatment in 99% N2/1% O2 reduces Tc to 123 K and increases the a parameter to 3.862 Å. An additional 10 h reduction in a 100% N2 flow lowers Tc to 98 K while a increases to 3.865 Å. Subsequent oxidation at 300°C for 10 h in O2 flow restores the lattice parameters and Tc onset to their original values. The Tc dependence on annealing conditions is shown to be reversible.