OKay - you found some killer heads today! They are all good ones!!! Here is a quick rundown.
You actually have two different generations of the same shell with the SMOKELESS and ARROW. The UMC SMOKELESS is the grandfather of the Rem-UMC ARROW.
The UMC SMOKELESS was introduced in 1891. It was sold under the name SMOKELESS until 1901/02 when UMC changed it's name to ARROW. The ARROW LINE was a carryover line when UMC and Remington merged in 1911. Remington-UMC kept the ARROW line around until the mid 1920's. I believe 1923 was the last year, but I cannot find my notes right now.
Your LIBERTY head about knocked me out of my chair. It is the first one that I have ever seen! According to a popular website, the date range is 1908-1917. I have not researched this line of shells, so I have VERY limited information on them. I do know that the Liberty Cartridge Company was listed in the 1909 District of Columbia directory. Sort of interesting that a ammunition company from the capital city of the United States is called "Liberty".
Now the short answer:
UMC Smokeless - 1891-1902 (very scarce find)
Rem-UMC Arrow - 1911-1920's (uncommon but not rare)
Liberty Bulk - 1908-1917* (very rare - first I have ever seen)
Those are some GREAT finds!
Doug
Will PM you later this evening.