```python
def cross_up(readings: list, level: int) -> int:
    """
    Count the number of times a run of readings crosses a level going upward.
    
    Args:
    readings (list): A list of integers representing the readings.
    level (int): The level to cross.
    
    Returns:
    int: The number of crossings.
    """
    if not readings or level <= 0:
        return 0
    
    crossings = 0
    for i in range(1, len(readings)):
        if readings[i] > level and readings[i-1] <= level:
            crossings += 1
    
    return crossings
```