When people learn about polyamory, one of the first responses is often about being "too jealous for that sort of thing". When you speak further with them about what they mean by being jealous, the underlying feeling is frequently more like possession. This points out a really ugly thing that most of us don't want to admit: We're pretty well programmed to think of our mate(s) as something we own.
Once the concept sinks in, you have the choice to be OK with your programming, or try to set up some new code (Notice the computer speak here. It was inevitable after hanging out with these two!). If you opt to treat your partner(s), even within your internal monologue, as a being with free will that is capable of going somewhere different at any point in time, then you can really begin the work!
See, the whole point of "owning" your partner has to do with the fear of being left. If you own something, you control it. The tough fact is that, while you can lay claim to the relationship you share with someone, the person you share it with is totally autonomous. Yep, that's right. They can exercise the option to walk at any time.
How does this allow anyone to be open and trusting? When can you reach a point of feeling safe within a relationship? This is the point where you take a combination of intellect: Do their actions back up what they say? Do they take care of themselves? Do they handle various obligations well? add in intuition: Is there that nagging sense that something isn't as it appears? Do you feel joyous when you think of them? Do they seem considerate of you and your feelings? then you add in that last element, faith. Sometimes you just have to jump in, hope, and be open. Trust that you are making the best decisions you can based on what you know, and that you can change your mind later, if you know better on down the road.
Yes, you might be left. Yes, you might be in a position where you decide to do the leaving. Yes, you are the one person in the whole world that you can possess. The quest is to try to make yourself someone worthy of the love you seek and share with yourself and others.