If the person you invited doesn't yet have an Airstory account, s/he can view your document (without creating an account) by clicking on the green 'Go To Document' button:
You can invite as many guests as you like to your projects, and they'll be able to collaborate with you at no cost (to you or to them).
When you invite guests to your Airstory projects, you can set their role to "View Only", "Researcher" or "Editor". Learn more about user roles here.
The only restriction on guests is that they cannot create their own projects, or administer yours (e.g., invite others or delete your project).
Guest users have 5 days to turn their temporary account into a permanent account by selecting 'Just create a free Airstory account now' in the bottom right-hand corner of the Airstory interface: