Reference to pointer to const as function argument

I have the following base code:

Base Code

int main()
{
  int i = 1;

  const int* p = &i;
  int* q = &i;

  test_ptr(p);
  test_ptr(q);
}

Can anyone explain why the first and third example work with the above base code, but the second one doesn't?

Example Implementation test_ptr()

Example 1 works. This works because function with pointer to const int will also accept a pointer to non-const int (but not the other way around)

void test_ptr(const int* p)  // pointer to const int
{

}

Example 2 doesn't work. I don't really understand why. It is still a pointer to const int, but passed as a reference. This doesn't align with my understanding about how references work. It fails when I pass a non-const pointer to the function.

void test_ptr(const int*& p)  // reference to pointer to const int
{

}

Example 3 works again and I am completely lost. So if case 2 does not work, why does it work again if I express the int* as a typedef?

typedef int* int_ptr;

void test_ptr(const int_ptr& p)  // like case 2 but int* expressed as typedef
{

}

This also happens when I use pointer-to-pointer instead of reference-to-pointer.

Edit: Example 3 needs a different main function to make use of the typedef:

int main()
{
  int i = 1;

  const int_ptr p = &i;  // use typedef here
  int_ptr q = &i;  // use typedef here

  test_ptr(p);
  test_ptr(q);
}