While the experience of your app could benefit from animations, sudden movements could cause, for example, dizziness, vertigo or nausea for some of your users. Here's a strategy to deal with this.
(Modal) dialog windows
A modal dialog requires a user's response and makes it mandatory to interact with it. Focus, both literally and proverbially, can't be moved away from the modal. Learn more about what to look out for when using dialog windows
Notifications for all users
You have to inform every user about dynamic changes in your web app - not just the ones using a visual browser. Learn more about programmatically exposing asynchronous content changes to screen readers
What makes web-apps special?
Web applications aim to emulate the experience of native apps by loading and displaying data in an asynchronous fashion ("AJAX"). This lack of full page reloads makes it hard for users of screen readers.
The Demo App "Accessibooks"
Reading about patterns in theory only gets you so far – often times you need a concrete example to learn. This is why Accessibooks SPA exists.