Infantry to Artillery (for a basic example, let's use New York):
19th Infantry - 3rd Light Artillery
113th Infantry - 7th Heavy Artillery
129th Infantry - 8th Heavy Artillery
135th Infantry - 6th Heavy Artillery
138th Infantry - 9th Heavy Artillery
Infantry to Cavalry:
130th Infantry - 19th Cavalry
Cavalry to Artillery:
(hardly ever, only example I remember is the SC battalion Rutledge Mounted Rifles to Horse Artillery)
Cavalry to Infantry:
(almost never, usually just temporarily as dismounted, most prominent in the Trans-Mississippi)
Artillery to Infantry:
2nd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 14th, and 15th New York Heavy Artillery - Infantry from Spotsylvania onward
Artillery to Cavalry:
(never?)
-Stryker