Since this is being bumped, I'll throw in my two cents. I experience this primarily as a poly-curious person navigating first steps, but I've done a lot of the recommended poly reading.
Embrace your emotions. Don't try to resist them. They're trying to tell you something about yourself. Allow yourself to feel your emotions. The more you feel them, the less power they have over you.
This is absolutely critical, and I might even move this to the top of the list instead of the bottom to encourage healthy, individual, intentional self-regulating over less effective modes of preoccupied co-regulating or avoidant auto-regulating. As always, there's no shortcut for doing the work.
If managing anxiety is important to you, then it's important that you get better at self-soothing. As you let your emotions in, you get better at resolving them, and you get better at not relying on others to co-regulate. Yes, anxiety can have a root cause or be based on irrational fears. But beyond trying to problem-solve your anxiety out of existence, it usually happens that a garden variety thought comes first, the feeling in your body comes second, and the emotion interpreted as anxiety comes third.
Not to say you shouldn't make your anxiety visible to your partner if they are having trouble seeing it or are clearly causing it negligently or unknowingly, but I'd caution against asking your anxiety what it needs too early in the temper tantrum it's throwing. The first answer isn't always the right one.
I wanted to share my trouble connecting to my feelings before they get so big:
Does anyone else's brain do what mine does when I'm anxious? It starts regurgitating garbage: bits of old movies, musicals, songs, commercials, odd geometric oddities, half-baked inventions, and other distractions. It tries to throw up a smoke screen of noise to drown out the anxiety. Even if I ask my anxiety what it needs, I'm not going to hear it over the fucking
TripleDent Gum jingle. It's gotten to the point that I if I notice any intrusive random thought, I check in with my anxiety and unusually find it starting to bubble up. It's a lot easier to feel and soothe at that stage than in a full-blown spiral.