Here we investigate the complex relationship between the growth conditions and the structural and transport properties of Ti<sub>x</sub>O<sub>y</sub> thin films grown by molecular beam epitaxy. Transport properties ranging from metallicity to superconductivity and insulating states are stabilized by effectively tuning the O/Ti ratio via the Ti flux rate and the O partial pressure P<sub>Ox</sub> for films grown on (0001)-Al<sub>2</sub>O<sub>3</sub> substrates at 850° C. A cubic c-TiO<sub>1±δ</sub> buffer layer is formed for low O/Ti ratios, while a corundum cr-Ti<sub>2</sub>O<sub>3</sub> layer is formed under higher-oxidizing conditions. Metallicity is observed for c-TiO<sub>1-δ</sub> buffer layers. The superconducting γ -Ti<sub>3</sub>O<sub>5</sub> Magnéli phase is found to nucleate on a c-TiO<sub>1-δ</sub> buffer for intermediate POx conditions, and an insulator-superconducting transition is observed at 4.5 K (T$^{onset}_{C}$ = 6K) for 85 nm thick films. Strain relaxation of γ -Ti<sub>3</sub>O<sub>5</sub> occurs with increasing film thickness and correlates with a thickness-dependent increase in T<sub>C</sub> observed for Ti<sub>x</sub>O<sub>y</sub> thin films.