What area of medical practice deals with the supply of blood,oxygen and iron to the head,brain?

I observe that anxiety and depression might be due to shortage of blood or oxygen or iron to the head and brain

Hematology deals with the blood and its compnents. Cardiology deals with the circulatory system and neurology deals with the central nervous system (brain,spinal cord,cranial and spinal nerves)

This would be neurology or even a vascular doctor since you are referring to blood flows.

Sorry, none of them deal with that, specifically. Neurologists deal with the brain, hematologists deal with blood disorders, and pulmonologists deal with oxygen issues.

What do you mean "you observe . . ." If your brain is short on oxygen you have what's called a stroke. If you have iron deficiency, it can certainly cause problems, but to my knowledge there have been no studies linking iron deficiency to anxiety/depression.

Most likely a vascular surgeon (or cardiovascular surgeon) if you are referring to someone who has had a carotid doppler and is in need of an endarterectomy (surgery to increase the blood flow).

In terms of the effects in conditions where blood flow deficits have resulted in a stroke or dementia, probably a neurologist.