The brief summary (does not apply to all cases, especially not to some older cases):
1) Look at the square part of the reed, where the rivet goes through. If the sides are blue then the reed is made out of a narrow ribbon steel and is hand made (a mano).
2) If not 1) then if the rivet has marks of being tightened by hammering (with a hammer) around it (so it may show 6 or more marks) then it is a hand-finished (tipo a mano) reed.
3) If not 2) then the rivet is just round and has received blows straight down by a "machine gun" and the reed is a machine-reed (which you call "factory reed", but all reeds come out of a factory nowadays, also the hand made ones).