2001 trucks can run either 2001 or 2002 OS's, however three unique OS's exist for 2002 trucks, Allison/Push button transfer case, Allison/manual lever transfer case, ZF-six speed/manual transfer case and there is a Federal OS, Northeast OS or a California Emissions OS.
2003-2004 there is a Federal OS, Northeast Emissions OS and a California OS, the same three unique OS's apply for your transmission/transfer case combo.
In the case of the 2003-2004 LB7/OS you have to pay attention to extra's like ON-Star, climate control, cruise control, etc. Use the wrong OS/Segments and those may quit working. Use the wrong segment for the engine and it may throw codes for glow plugs, etc.
You can mix and match but the two OS's have to be compatible to compare and swap or else you can have non-working components.