I think the proper designation for 1 guards mixed air corps is 1GIAK. Air corps were specialist or separately designated units not to be confused with Regiments.
Stalins Eagles lists 1IAK as becoming 1GIAK ON 3-18-43 it was based in Beletskij from Oct 42 until the end of the war. No listing of Zajtsev
SE lists V A Zajtsev as Podpolk of 105 GIAP but can give no other history to the regiment.
He is listed as being with regiments 129IAP which became 5GIAP ( with Popkov etc) before being bumped up stairs to be assistant commander of 11GIAD. Which is a Division! ( Wing or Group) Which at the time had many Regiments under it.(Regiments were assigned to Divisions)
11 GIAD was formed from 207IAD on the 8-24-43. It was part of the 2VA and latterly the 17VA (air armies). One of the regiments assigned to 11GIAD was 5GIAP. If you look to the history of 5 GIAP you will note that the Podpolk from sep 42 to April 44 was a VA Zajtsev.
He was replaced by Popkov (see our La5FN skin white 01) This was (some say)
the most successful Regiment in the VVS!
on the other hand 1GIAD was formed from 220 IAD. It is not the same as 1GIAK.
there was a 1GIAD-KBF of the red banner fleet (Baltic) it had regiments assigned to it such as 5,13,&71IAP and was later reformed as 3GIAD-KBF. It is credited with the arial defence of Lenningrad.