What type of arbor should I use to fix this holesaw?
For that type of setup, you usually use this type of bit.



The nut on the shank side screws off, then the bit slips into the hole saw and the nut is tightened back down to hold the saw in place.  I found this one at ACE Hardware. But they should be available at any hardware store.

Your best bet would be to take the hole saw with you to the store, and ask an associate to help you find what you need.  I found it online using the search term Vermont American #18303 Mandrel.