I started to research this earlier, went away, and came back to find that others were reaching the same conclusion. The dictionary definitions of "acezar", breathe heavily/pant or long for/strongly desire, make no sense at all hrtr. But somehow, quite probably by the route Lorena suggests (acceder > accesar > acesar > acezar), it comes to mean the same, apparently, as "acceder". There are really quite a number of examples, all American, I think:

"Modulo de Acceso y pagos en línea [...]
Como funciona
El cliente podrá acezar al sitio y por sus datos el sistema le indicaría lo siguiente: "
http://www.sicamexico.com/pagos-en-linea.html

It can also be used sometimes without "a", apparently:

"Los motoristas que viajan hacia el este por la Calle 25 del noroeste y desean acezar la Avenida 37 del noroeste serán dirigidos a tomar la Avenida 39 del noroeste rumbo norte hasta la Calle 27 del noroeste rumbo oeste."
http://www.miamidade.gov/transit/releases/11-05-20-traffic_a...

Here's another:

"Al acezar nuestras páginas de internet se genera de manera automática (sin necesidad de tener que registrarse) un almacenamiento de informaciones que no se pueden adjudicar a una persona en particular"
http://es.germancentre.com.mx/impressum

Used transitively like this it seems to be a calque of the English "to access".

More examples apparently meaning "acceder a":

"Por ejemplo; si lo que deseas es comprarte un carro nuevo, entonces puedes decidir incluir en la descripción el tipo de carro (deportivo, sedán, camioneta…), el color y el rango de precio al que deseas acezar…"
http://www.radiomenteabierta.com/emprendedor/archives/2910

"si usted ha pensado en tatuarse piénselo, no se valla [sic] de las primeras, sus oportunidades de acezar a una empresa de prestigio se verán minimizadas, debido a que llevar un tatuaje no inspira confianza en su persona pone en duda la seriedad e integridad de sus actos."
http://es-es.facebook.com/notes/búscame-y-te-encontraras/tat...

There are quite a lot more like this. All seem to be Mexican, as far as I can see. The meaning is pretty clear, I think.

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Note added at 12 hrs (2011-10-14 06:52:42 GMT)
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To be more accurate, it seems likely that "acezar" comes from a false coinage "accesar", from English "to access", reduced to "acesar", and then, by homophonic substitution (homophonic in Latin America, that is), to "acezar".

Here is a note on "accesar":
http://www.wikilengua.org/index.php/accesar

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Note added at 12 hrs (2011-10-14 06:59:02 GMT)
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The translation could be simply "access". "To access a place" can be said in English, and there are plenty of Google results for "access the mine". However, this use of "access" as a verb is not approved in careful style, except for accessing computer data. Personally I would prefer not to use it here.


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Note added at 12 hrs (2011-10-14 07:00:58 GMT)
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See here:

"What's your take on using the verb "access" when not referring to computer data?
E.g., how would it sound to say "homeless people can 'access' shelter in several different locations"?

I used to find that usage abhorrent, but it must be wearing me down. Bernstein says "It is not difficult to figure out the meaning of the verb: to gain access to, or to obtain or plain old to get [or to find in the sentence you offer]. But who needs it?" And the American Heritage manual says that 80% of its usage panel rejects the use of "access" as a verb (outside the realm of computerese). Personally, I'm still 80% against it.

Authority: Dos, Don'ts & Maybes of English Usage by Theodore Bernstein. Gramercy Books: New York. 1999.
Authority for this note: American Heritage Book of English Usage: Houghton Mifflin Co., Boston. 1996."
http://grammar.ccc.commnet.edu/grammar/grammarlogs4/grammarl...

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Note added at 12 hrs (2011-10-14 07:25:23 GMT)
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To sum up, this word illustrates an interesting phonological and syntactic process:
1. The new transitive verb "access" is introduced in English, by verbalising the noun "access". The usage become standard in computing and is widely used in other contexts too.
2. This new English verb is calqued in Spanish as "accesar", again used transitively: "accesar datos". The calque is presumably facilitated by the existence of "acceso". Again, it is also used in other contexts; a few cases of "accesar la mina" can be found, for example.
3. The verb "accesar" is assimilated to the syntax of "acceder", and "accesar a" (intransitive) becomes much more common than "accesar" (transitive). There are more cases of "accesar a la mina", and also of "accesar a datos".
4. "Accesar" becomes reduced to "acesar" in speech. This spelling is found, though it is uncommon.
5. Latin American speakers, who pronounce "accesar" as /aksesar/, reduce this to /asesar/.
6. This is assimilated in writing to the existing Spanish verb "acezar", which in Latin America is also pronounced /asesar/.