Glycolysis can occur without the presence of oxygen, while the other steps in respiration (PDH complex, Kreb's cycle and oxidative phosphorylation) all rely on the presence of oxygen either directly or indirectly.
If you are undergoing respiration in completely anaerobic conditions (no oxygen), then glycolysis is the only process that would occur to create ATP needed for the cell. Glycolysis would probably occur more during anaerobic conditions than when oxygen was present simply because the cell has to rely only on that to make ATP.