CSS transition between two SEO-friendly webpages

Question

My Goal:

Let's say I've got two webpages page1 and page2. Now, I would like to have an animation (using css transition) to transform page1 into page2 or page2 into page1 if the user navigates from page1 to page2 or from page2 to page1 respectively. Moreover, I would like that search engines can find both pages.

My Problems / What I've tried:

1. Use actually only one page page.html with hashes: page.html#page1 and page.html#page2. For example by listening for a hashchange event the transition can be done easily.

2. Use parameters: page.html?content=page1 and page.html?content=page2. A complete reload of the page can be avoided by the preventDefault method or history.pushState.

As far as I know, in the first solution, search engines are not going to show my pages as separate links. Also, both solutions have the following major problem: What happens if someone writes simply page.html into the browser's address field or – even worse – page.html appears as a link in search results? I really would like that page.html doesn't exist at all, but that seems impossible given the above solutions.

So, the best solution I could think of so far, is having actually two pages page1.html and page2.html that have both exactly the same content (that is, the content of both pages combined). E.g. in page1.html the content of page2 would have property display: none. Now, when a user navigates from page1 to page2, I use history.pushState to set the new URL. While I believe this should in principle work, I'm concerned about having two identical pages or hiding large amounts of a page using display: none as both is supposed to be bad for SEO.

Any answer that addresses at least part of my problem is very welcome! Maybe there is a way to at least prevent search engines from finding page.html in my second solution? Or maybe there is a solution I'm completely unaware of?