[css-view-transitions-2] Separte MPA transition start from check (#9819)

* [css-view-transitions-2] Separte MPA transition start from check

* change algorithm title

* Change things a bit

* nits

Author: noamr

css-view-transitions-2/Overview.bs

@@ -557,28 +557,31 @@ When capturing the old or new state for an element, perform the following steps
 ### Setting up the view-transition in the old {{Document}} ###  {#setup-old-document-vt}
 
 	<div algorithm>
-		To <dfn export>setup cross-document view-transition</dfn> given a {{Document}} |oldDocument|,
-		a {{Document}} |newDocument|, a {{NavigationType}} |navigationType|, a boolean |isBrowserUINavigation|, and |onReady|, which is an algorithm accepting nothing:
+		To check if a <dfn export>navigation can trigger a cross-document view-transition?</dfn> given
+		an [=origin=] |oldOrigin|, an [=origin=] |newOrigin|, a boolean |navigationHasCrossOriginRedirects|, a {{NavigationType}} |navigationType|, and a boolean |isBrowserUINavigation|:
+
+			Note: this is called during navigation, potentially [=in parallel=], for documents that have opted-in to view-transitions using the ''@view-transition'' rule.
 
 		1. If the user agent decides to display an [=implementation-defined=] navigation experience, e.g. a gesture-based transition for a back navigation,
-			the user agent may ignore the author-defined view transition. If that is the case, return.
+			the user agent may ignore the author-defined view transition. If that is the case, return false.
 
-		1. If |navigationType| is {{NavigationType/reload}}, then return.
+		1. If |navigationType| is {{NavigationType/reload}}, then return false.
 
-		1. If |isBrowserUINavigation| is true, and |navigationType| is {{NavigationType/push}} or {{NavigationType/replace}}, then return.
+		1. If |isBrowserUINavigation| is true, and |navigationType| is {{NavigationType/push}} or {{NavigationType/replace}}, then return false.
 
-		1. If |oldDocument|'s [=environment settings object/origin=] is not [=same origin=] as
-			|newDocument|'s [=environment settings object/origin=] then call |onReady| and return.
+		1. If |oldOrigin| is not [=same origin=] as |newOrigin| then return false.
 
-		1. If |newDocument| [=was created via cross-origin redirects=] is true
-			and |newDocument|'s [=latest entry=] is null, then call |onReady| and return.
+		1. If |navigationHasCrossOriginRedirects| is true, then return false.
 
-			Note: A document with a non-null [=latest entry=]
-			is being [=Document/reactivated=], in which case we don't need to check for cross-origin redirects.
+		1. Return true.
+	</div>
+	<div algorithm>
+		To <dfn export>setup cross-document view-transition</dfn> given a {{Document}} |oldDocument|,
+		a {{Document}} |newDocument|, and |onReady|, which is an algorithm accepting nothing:
 
-		1. [=Resolve @view-transition rule=] for |oldDocument| and let |resolvedRule| be the result.
+		1. Let |resolvedRule| be the result of [=Resolve @view-transition rule|resolving the @view-transition rule=] for |oldDocument|.
 
-		1. If |resolvedRule| is "<code>skip transition</code>", then call |onReady| and return.
+		1. If |resolvedRule| is "<code>skip transition</code>", then return null.
 
 			Note: We don't know yet if |newDocument| has opted in, as it might not be parsed yet.
 			We check the opt-in for |newDocument| when we fire the {{Window/pagereveal}} event.
@@ -644,6 +647,8 @@ When capturing the old or new state for an element, perform the following steps
 			* its [=active view transition=]'s [=ViewTransition/phase=] is "`done`".
 
 			Note: this is to ensure that there are no unintended flashes between displaying the old and new state, to keep the transition smooth.
+
+		1. Return |outboundTransition|.
 	</div>
 
 ### Accessing the view-transition in the new {{Document}} ### {#access-view-transition-in-new-doc}