Gingivitis' suggestions are good. I'll also point out some hints that the book offers. Let's look at a few of the spells listed:
Target Self / Willing Target
Physical Mask - reroll 2 Disguise dice
Improved Invisibility - reroll 2 failed Stealth dice
To me, it seems like spells directed at willing targets should not be resisted, since their mechanical effect is to boost the target's skill rolls. Should the player succeed with those rolls, the narration can give credit to the spells. If the character fails with those rolls, the narration can either say that the opposition was not fooled or that some other element (e.g. footsteps, or the wrong behavior) gave the character away.
That begs the question of what the spells should be resisted by. I don't know the answer. Since there's not a lot of consequences to failing a casting (no drain or any other downside), it may not make sense to have any roll unless you're looking for things to inform the narration. ("Oops, failed, that was embarrassing," etc.)
Unwilling Target
Chaotic World - targets must reroll 1 successful die per roll
Confusion - target suffers -1 penalty to rolls
Illusion - same as Confusion (from Razzle Dazzle's shadow amps)
These spells, since they have third-party targets, seem like they should follow the guidelines for Combat spells and be resisted by the opposition. (The players would want rolls to resist if they were targeted by these spells, presumably.) For these, I would follow Gingivitis' suggestions. I would probably opt for #3 myself, since the dice rolling inherent in #2 is unpalatable to me and is at odds with the goals of Anarchy. It requires the GM to track who was affected and who was not, then have each individual respond accordingly. That's a lot of work and not at all conducive to keeping things moving forward.