How can I know if North Atlantic Tracks have been amended? Information about the North Atlantic Tracks is issued through Track Messages. The NAT Doc 007 document states that every track message is identified by the TMI (Track Message Identifier) number:

The originating OAC identifies each NAT Track Message, within the
Remarks section appended to the end of the NAT Track message, by means
of a 3-digit Track Message Identification (TMI) number equivalent to
the Julian calendar date on which that OTS is effective. For example,
the OTS effective on February 1st will be identified by TMI 032. (The
Julian calendar date is a simple progression of numbered days without
reference to months, with numbering starting from the first day of the
year.).

In case the North Atlantic Tracks are modified, a letter is appended to the TMI number:

If any subsequent NAT Track amendments affecting the entry/exit
points, route of flight (co-ordinates) or flight level allocation are
made, the whole NAT Track Message will be re-issued. The reason for
this amendment will be shown in the Notes and a successive alphabetic
character, i.e. ‘A’, then ‘B’, etc., will be added to the end of the
TMI number (e.g. TMI 032A).

I would like to know how such change is notified to the interested parties; is some ATCs issuing a NOTAM to declare that some changes have been done to the TM? If yes, where can I visualize such NOTAM?
One possible way to overcome my problem would consist in constantly checking if the TMI number has changed but this is not a very efficient way to proceed. I would rather expect some NOTAM which notifies the TMI number change.
Can you tell me if what I ask is plausible? If yes how can I proced?
For starters I am not completely knowledgeable with the North Atlantic Tracks but work with some of the other Flex track systems in the world. And they are all very similar.
The Track Messages are a type of NOTAM. They are released everyday and revised NOTAM (Track Message) is released if there are changes. They increment the alphabet character on the end of the TMI so that when a clearance is   issued by Air Traffic Control(ATC) they know which track they are flying including the version and ATC can correct it if the pilot has old information.
Extract from one of the Track Message:

REMARKS.

TMI IS 013 AND OPERATORS ARE REMINDED TO INCLUDE THE TMI NUMBER AS
PART OF THE OCEANIC CLEARANCE READ BACK.


When there is any changes they reissue the entire NOTAM (Track Message). So requesting accessing the message again will tell you straight away what is current. Usually aviation doesn't care about what it was, only what it is and what it will be. The computer systems that the airlines use get the most up to date data when they create the Flight Plans.
The question is what you want to do with the data to how the best way to get the data. But the link you supplied will always have the most recent ones.
Visualization of the these tracks, plus others, can be done on SkyVector. Go to layers to change any settings. The link automatically loads up on an ERC High with North American and Pacific Tracks Selected.