This seems to work:

First, give your annotations a div id as outlined in the comments by janani in this post:

Annotation gap

In my instance I made a blue info box annotation with the following entry

<div id="anno1">Test annotation</div>

Next, write a client script to fiddle with it. I wrote mine as an onLoad script but I did a quick test using onChange and it seemed to work there too.

function onLoad() {

    //Type appropriate comment here, and begin script below

    document.getElementById("anno1").parentNode.style.display="none";

}

Hope that works for you