Some locals have their tool list posted on their website. Usually in a dispatch or job postings section of the website. It usually there to make sure any travellers coming into the local can get the list easily.
To answer the other part, the union wants everyone to have the same basic hand tools. If the employee requires other specialized tools then the employer will provide them.
The reasoning is two part........
1 It shouldn't cost you, the employee, a small fortune in tools just to go to work. You only need the basics.
2 The guy working next to you wont have any unfair advantage come layoff day.
For example...........
"Joe has twelve tool boxes full of speciality tools that we need next week so we can't lay him off......Fred only has the basics and everyone has those so we can afford to let him go".
NOW......let the union bashing begin.