Anesthesia coding is not my specialty, so maybe other posters will respond. But as I understand it, you would not use the surgery times to determine anesthesia time - you would need to use what the anesthesiologist documented for their own services.
Per CPT, "Anesthesia time begins when the anesthesiologist begins to prepare the patient for the induction of anesthesia in the operating room (or in an equivalent area) and ends when the anesthesiologist is no longer in personal attendance, that is, when the patient may be safely placed under postoperative supervision."
So by this definition, you do have a stop time here, 11:45am, but you don't have a start time because you haven't stated when the anesthesiologist began to prepare the patient. You would need that in order to calculate your time.