Merging two previously sorted singly linked lists

I am currently trying to write a function to merge two linked lists that have been already sorted. However I am experiencing trouble. So far I have the following:

void list::mergeLists(const list &L1, const list &L2) {
     Node* pointer1 = L1.head;
     Node* pointer2 = L2.head;
     Node* pointer3 = NULL;

     if(pointer1 == NULL) {
          while(pointer2 ->next! =NULL) {
               pointer3 = new Node;
               pointer3-> data = pointer2->data;
               pointer3->next = head;
               head = pointer3;
               pointer2= pointer2->next;
          } 
       } 

    if(pointer2 == NULL) {
          while(pointer1 ->next! =NULL) {
               pointer3 = new Node;
               pointer3-> data = pointer1->data;
               pointer3->next = head;
               head = pointer3;
               pointer1= pointer1->next;
          } 
      } 

}

so as you can see the only case I have is that if one of the lists are empty and this does not produce expected results. It produces a result that that reverses the lists and leaves off the last item. Please help me to fix this problem and move forward into merging two lists.