Exercise generally acidises the blood. I'm looking for information on the timing of onset and how long this lasts after the exercise. Furthermore, I'm looking for info on alkalization of blood caused by exercise. What might be the reason for this? Lactic acid seems to play a role in the acidization, right? Are there conditions where exercise might lead to a rise in pH? Can, in untrained people or those who don't build up enough acidity heavy breathing be enough to shift blood pH towards the alkaline range? McArdle comes to mind, but I can't find any actual sensitivities on this.
I am unaware of any mechanism by which exercise can cause "blood alkalization" (usually called "alkalosis").
Blood pH is VERY tightly regulated at 7.35-7.45 (slightly alkaline), so it rarely changes much except in severe illness.
That said, slight acidosis can occur in exercise due to an increase in carbon dioxide released from muscles (Medline Plus - Respiratory Acidosis). Onset would depend heavily on a person's conditioning and the intensity of exercise, with poor conditioning and high intensity being associated with faster onset. In most cases, any acidosis would dissipate quickly after stopping exercise - i.e. within minutes. After heavy exercise it may take a bit longer. (PubMed - Acid-base regulation during exercise and recovery in humans)
Over production of lactic acid may also cause acidosis during exercise, but this is up for debate (this BMJ article says yes, whereas this review from the American Journal of Physiology says no, for example). In any case, severe lactic acidosis occurs much more commonly due to serious diseases like AIDs, sepsis, or kidney failure (Medline Plus - Lactic Acidosis).
Further, heavy breathing in exercise doesn't "build up acidity", it counter-acts acidosis by getting rid of the excess carbon dioxide. Severe hyperventilation not during exercise (e.g. during a panic attack) can cause slight alkalosis because it causes a person to exhale more carbon dioxide than their body is producing (Medline Plus - Respiratory Alkalosis).
In addition to the links above, I suggest you look at these Medline Plus pages; they do a good job explaining blood acidosis and alkalosis: