I think this is what you are looking for (check out the answer by BalusC) -
Whats the correct way to create multiple instances of managed beans in JSF 2.0
And since you are using @NoneScoped (unlike @RequestScoped in the above question), I also recommend you to look at this answer by BalusC (about @NoneScoped) -
what is none scope bean and when to use it?
And according to this answer, you can't maintain any instances of a managedbean that is none-scoped, as they are garbaged as soon as they are used.
So, in your case since you have three separate views, for each view, the bean is constructed and used to build the view and garbaged. (Looks like it does not even last for a request cycle). When you request another view, it will be a separate instance.
To have multiple intances of a bean, you can have three properties in a Session-Scoped
been (to make them survive across multiple views).
@ManagedBean
@SessionScoped
public class Parent {
private Child child1;
private Child child2;
private Child child3;
// ...
}