Is there a way to hide annotations from other pieces while working on the current document?
Yes. When creating a new incoming link on a Reference document, use the Filter menu to hide some or all existing incoming links on the reference document that is viewed within the mini-browser. To temporarily hide them all, unselect Show Incoming Links.
Show or hide incoming links from specific documents by clicking Filter Incoming Links and then unselect specific documents. Also note that with Enhanced Annotations (available as a configuration in Vault), an existing incoming link can be reused (reselected) when creating new links on any document.
Note that incoming links are renamed anchors in Enhanced Annotations.
Vault Annotate Documentation: Using Link Annotations & Document Links