Ok good !
Yes the status is completed.
I did add new required fields in reservation.class.php and in include/classes/PaymentIPN.class.php.
The problem is that with authorize, it seems we cannot use both relay and receipt method. it is necessary to have fields in apphp api 's form.
I think that by the past they nativly went back to apphp web site with the referer's url.
Now, this url has to be written/declared in the apphp's form and setted with authorize. So relay can't be use to send transaction info because it shoud be use for return.
The link index.php?page=booking_notify_autorize_net can't be open on my way with browser. It should be the same for authorize wich send error message.
So we shoul use silent post url to set index.php?page=booking_notify_autorize_net and have transaction's return.