I am no expert, but as far as I know, IOS does not have activities like Android has. IOS has controllers (e.g. NavigationController is the default) that manage pages.
The page does have an Appear and Disappear event that you could use.
The NavigationController puts pages in a stack, and provides navigation (pop) back to the previous page. If you ShowPage a page already in the stack, all the pages added after that page will removed from the stack (e.g. if you return to your main page via ShowPage(Page1), all pages are removed from the stack and Page1 is shown again)
There is also a TabBarController available that you could use instead of a NavigationController. This controller allows you to switch pages by clicking on items in the tab bar.
As far as I know, these are the only controllers available now in B4I, maybe other IOS controller types will be added later.