sed and Multi-Line Search and Replace

I’ve been experimenting with getting regular expression patterns to match over multiple lines using sed. For example, one might want to change
<p>previous text</p>
<h2>
<a href="http://some-link.com">A title here</a>
</h2>
<p>following text</p>
to
<p>previous text</p>
No title here
<p>following text</p>
sed cycles through each line of input one line at a time, so the most obvious way to match a pattern that extends [...]