Step 1: Understanding the pericyclic reactions.
The transformation involves a series of pericyclic reactions, including electrocyclic ring opening and sigmatropic shifts. In this case, the correct mechanism involves the following steps:
1. A 6 \( \pi \) electrocyclic ring opening leads to the formation of an intermediate.
2. A [1,7] sigmatropic shift then occurs to complete the transformation.
Step 2: Conclusion.
The pericyclic reactions that occur in the synthesis of Vitamin D\(_2\) from Ergosterol are correctly described by option (A), with a 6 \( \pi \) electrocyclic ring opening followed by a [1,7] sigmatropic shift.
Final Answer:
\[
\boxed{\text{6 } \pi \text{ electrocyclic ring opening followed by [1,7] sigmatropic shift.}}
\]