Unfortunately if the cat's anemia has gotten to the stage where a blood transfusion is required, then it's condition has been diagnosed as 'life threatening'.
The blood transfusion is neither a definate, nor potential cure as the transfusion would only be performed to stabilise the cat for long enough to undertake further tests to determine the cause of the anemia.
The causes of anemia in felines could be one of many conditions i.e. Autoimmune disease, The feline leukemia virus, Blood parasites, Chemicals or toxins in the blood, or Neoplasia (cancer). Each of these conditions would cause further investigation, then treatment, all with no guaranteed resolve.
All of this time the cat will be in a vet's cage, being fed through a drip and experiencing a very low quality of life for no guaranteed change in condition, let alone a percentage cure.
Yes, the cat is young, but this situation in my opinion is far beyond the surmised "I can't afford vet bills, hence putting my cat down".
Sorry to hear of your situation OP - I lost my dog of 3.5 years to pancreatitus; we forked out a lot of money to a vet who was very positive of full recovery, only to find his chances moving from 90%, to 50%, to 20% over the space of 3 weeks. Our family was devastated to have had our little spaniel suffering for those last few weeks and now feel that it is paramount to consider the welfare of the pet above any other factors.