I am glad you asked this question.  I don't think people realise how dangerous anesthesia can be for people with moyamoya.  Especially doctors that are not familar with MM. 
Most all anesthesia drugs causes everything in the body to slow down.  In order to do this, these drugs cause vasoconstriction.  The blood vessels constrict, heart rate slows down, breathing is slowed becasuse the muscles that allow us to breath are slightly paralized, blood pressure is lowered, and body temperature usually drops slightly. 
People with moyamoya walk a very fine line between blood pressure being too low or too high, vessles constricting just enough or too much.  Most peoples bodies can with stand these fluctuations but many with moyamoya can only handle slight fluctuations in heart rate blood pressure etc...  So, having an anesthesiologist who is familar with moyamoya and knows how to regulate medications to allow you to be sedated without going over board is really important. 
I have moyamoya and just had surgery less than two weeks ago.  I spent a lot of time with our anesthesia team teaching them about moyamoya and they took the time to research the disease as well.  They were extra causious, they gave me extra fluids before surgery to boost my blood pressure, they used an arterial line to monitor my B/P more closely.  They did a really good job.  I also spent the first night after surgery in the ICU instead of the surgical floor so that I could be monitored more closely while the anesthesia was wearing off, which can take a couple days.  This was a good thing for me because at about 3am by blood pressure dropped dangerously low.  Since I was in the ICU hooked up to monitors they were on top of it immediatly which may have saved me from having a stroke.  I live in a small town and my surgery was done at our local hospital, but since my surgeon, the anesthesiologist, and the hosptial nurses were willing to listen to me and do some research on there own my surgery was very successful.  We do not have a neuro department at my local hospital.  If I had developed any complications they would have had to transfer me to a hospital 4 hours away. 
I hope this answers your question.  If you have any other questions about this topic just let me know and I will try to explain for get an answer for you. 
Take care and God Bless!!!

Tracie