In a person with sleep apnea, what causes the rises and falls in oxygen saturation of arterial blood during sleep?

Lack of oxygen: When you stop breathing (apnea) oxygen and carbon dioxide do not exchange in the lungs. Oxygen drops (hypoxia) and co2 increase (hypercapnia)... Classic response in a patient with apnea.

No breaths=no oxygen: This is caused by the temporary stoppage/blocking of breathing which is found in sleep apnea. Longer stoppage/blocking of breathing means less oxygen in the blood.

Sleep apnea: Sleep apnea is defined as stopping breathing for 10 seconds. During that time, the body is not getting any oxygen. In addition , there can be instances that last less than 10 seconds, or where a less than adequate effort to breath is attempted. These also reduce the oxygen intake.