When you implement rel="next" and rel="prev" on component pages of a series, we'll then consolidate the indexing properties from the component pages and attempt to direct users to the most relevant page/URL. This is typically the first page. There's no need to mark page 2 to n of the series with noindex unless you're sure that you don't want those pages to appear in search results.
In regard to using rel=”next” and rel=”prev” for entries in your blog that “are not strictly correlated (but they are just time-sequential),” pagination markup likely isn’t the best use of your time -- time-sequential pages aren’t nearly as helpful to our indexing process as semantically related content, such as pagination on component pages in an article or category. It’s fine if you include the markup on your time-sequential pages, but please note that it’s not the most helpful use case.
It sounds like your real estate rental site encounters many of the same issues that e-commerce sites face... Here are some ideas on your situation:
1. It’s great that you are using the Webmaster Tools URL parameters feature to more efficiently crawl your site.
2. It’s possible that your site can form a rel=”next” and rel=”prev” sequence with no parameters (or with default parameter values). It’s also possible to form parallel pagination sequences when users select certain parameters, such as a sequence of pages where there are 15 records and a separate sequence when a user selects 30 records. Paginating component pages, even with parameters, helps us more accurately index your content.
3. While it’s fine to set rel=”canonical” from a component URL to a single view-all page, setting the canonical to the first page of a parameter-less sequence is considered improper usage. We make no promises to honor this implementation of rel=”canonical.”
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