By resetting your resources, do you just mean all the items listed in step 4:
4.1 Drop cards from Hand 4.2 Remove cards from Play 4.3 Remove Time tokens 4.4 Remove Poison tokens 4.5 Reset Cards 4.6 Remove Lock tokens 4.7 Maintain Permanents 4.8 Draw up to your Hand Limit 4.9 Discard 4.10 END ROUND/GAME

Or do you mean the resources used to pay for crawler cards?
E.g. If a non controlling player plays magic long sword ( a non-permanent card) using 2 equipment resources, does that mean that they cannot remove the card from play until the end of the turn on which THEY are the controller? (Therefore in the meantime tying up the 2 resources used to pay for the card).