Does the anesthesiologist ever leave during the surgery?

No, an anesthesiologist or anesthesia care provider will be by your side for the length of the surgery. This is required because many physiological changes can occur under anesthesia and surgery, requiring constant monitoring and vigilance on the part of your anesthesiologist.  In some cases, another anesthesiologist may replace your anesthesiologist, but there is never a break in care as you are being monitored continuously for the entire duration of surgery.