Animals should have a pre anesthesia screening that should include blood work  
(CBC and Chem panels). Some anesthesia's are worked out through the liver and kidneys so proper function of them is needed. Checking the heart for proper function and even an EKG if any questions of rhythm may be done.

And if there have been any adverse reactions to anesthesia in your dog's past or in the dog's background, let the vet know and try to know what types of anesthesia they reacted to.

ACE (Acepromazine) is a sedative often given pre anesthesia or tranquilizer. Acepromazine lowers blood pressure and dilates blood vessels thereby making the blood pressure even lower.It also is metabolized (gotten rid of by the body) very slowly and tends to accumulate in fatty tissues. Therefore, larger dogs and fatter dogs usually have to be given a larger dose than normal in order to have effect, and because of this, it takes these dogs sometimes days to get back to normal. It is too unpredictable.

Atrophine was a drug that was used all the time as a pre-medication to dry up the saliva in dogs and cats and to keep the heart rate up. It is not used much anymore, or shouldn't be used in large and giant breeds. Atrophine causes the gut to slow down and this is not good especially in the mastiff. I believe slowing the gut down predisposes the mastiff to bloating.

Xylazine (Rompun) is another drug I avoid. It makes the heart more susceptible to the effects of epinephrine (adrenalin) that is in the body and therefore, making the dog more susceptible to heart abnormalities. It is a difficult drug to dose in giant breed dogs.

Acepromazine and Xylazine are the two drugs that I try to avoid if possible. If your veterinarian is also a large animal (cow, not mastiff) veterinarian, he may very well use the two drugs as they are used in farm animals a lot. If for some reason, your veterinarian must use these two drugs, I think it is mandatory that the dog be monitored by an EKG machine during surgery and immediately post-operatively.

Ketamine can be bad for dogs with liver or kidney disease question it with dogs prone to seizures as well.

Used the most in mastiffs are valium, ketamine, telazol, and propofol.
A combination of valium and ketamine given intravenously will be enough to knock the dog down in order to insert the endotracheal tube. Both of these drugs are very safe and I use them a lot in the older dogs. Neither one effect the heart much.

Telazol is very similar to valium and ketamine and also works well for anesthesia so that an endotracheal tube be place (I use .1 cc/lb and do not exceed 1.5 cc total).

Propofol (deprivan) for short procedures, i.e. OFA radiographs. Propofol is a fairly new
drug in the veterinary field but has been used for a long time in the human field. 
It is a milky solution that after opening a vial cannot be stored. It gets contaminated with bacteria very easily. Because it is expensive, the veterinarian may try to cut corners and use old leftover propofol that is sitting in the fridge. It is given to effect or in other words, it is given IV until the dog goes down and then the dog is intubated and put on gas. The GREAT thing about this drug is that as soon as the animal is taken off the gas, the dog is awake and can walk out without assistance. I have also used the drug in C-sections to sedate the dog long enough to insert the endotracheal tube. It is a very top of the line
drug. I do find the dosages of propofol to be a lot lower than the manufacturers literature dosage. One added thing: Propofol can lower blood pressure so the pet needs to be monitored while on that.

Oxymorphone for sedation and sometimes as the sole sedative for simple procedures like biopsy. It is an opiod and therefore it can cause respiratory depression, which means that the dog needs to be constantly monitored. There is a reversal agent called Naloxone that will reverse the effects of the drug and works quite well.Always put the dog on gas for a fairly short procedure. Isoforane is a gas of choice since it has fewer side effects. Halothane is still being used by some veterinarians. I do not use it since it (just like xylazine) sensitizes the heart which can cause irregular beats. But, as long as the dog is properly monitored, there should be no problem.

Isoflourae is a gas and is given through a face mask or trachea tube. It is often the anesthesia of choice as it is easier on pregnant animals (like if a c-section is done) and safer for animals with heart conditions. It is metabolized differently -  expelled through the lungs - and animals wake faster from it.

Prior to ANY anesthesia in any aged animal, I require a pre-anesthetic blood work up. I get a PCV (monitors whether anemic or dehydrated), a BUN (monitors liver and kidney function), Creatinine (monitors kidney function), ALT (monitors liver function), Alkaline phosphates (monitors liver and the biliary system), Total protein (monitors the immune system and hydration status), glucose and the electrolytes (sodium, potassium and chloride). I get these as I said even in young animals... It is just good medicine to know where the dog is prior to surgery and anesthesia so we will know how they will tolerate anesthesia. It is the base line. These test also guide me to my use of anesthesia. For
example, if there is kidney damage I know to avoid drugs that have to go through the kidney to be eliminated from the body. The temperature is also monitored along with the heart by an EKG.

There are loads of anesthesia's out there that work differently.