Step 1: Understand the disease named.
Pernicious anemia is a condition where the body cannot make enough healthy red blood cells, producing large immature cells. We need the vitamin whose lack causes it.
Step 2: Recall the role of vitamin $B_{12}$.
Vitamin $B_{12}$, also called cobalamin, is essential for the maturation of red blood cells in the bone marrow and for proper nerve function.
Step 3: Link the deficiency to the symptoms.
When $B_{12}$ is missing, red cells cannot mature properly and become abnormally large, which is the picture seen in pernicious anemia.
Step 4: Rule out $B_1$.
Deficiency of vitamin $B_1$ (thiamine) causes beri-beri, not anemia, so it is not the answer.
Step 5: Rule out $B_6$ and $B_2$.
Lack of $B_6$ leads to skin and nerve problems and lack of $B_2$ causes cracked lips and tongue inflammation; neither produces pernicious anemia.
Step 6: Conclude.
Therefore the vitamin whose deficiency causes pernicious anemia is
\[ \boxed{B_{12}} \]