PesistenceOptions is actually JQueryAjaxSettings.

backbone.js:Backbone.sync
> // Make the request, allowing the user to override any Ajax options.
> var xhr = options.xhr = Backbone.ajax(_.extend(params, options));

backbone/backbone-global.d.ts

@@ -41,11 +41,7 @@ declare module Backbone {
         parse?: any;
     }
 
-    interface PersistenceOptions {
-        url?: string;
-        beforeSend?: (jqxhr: JQueryXHR) => void;
-        success?: (modelOrCollection?: any, response?: any, options?: any) => void;
-        error?: (modelOrCollection?: any, jqxhr?: JQueryXHR, options?: any) => void;
+    interface PersistenceOptions extends JQueryAjaxSettings {
     }
 
     interface ModelSetOptions extends Silenceable, Validable {