The correct answer is option 4, which includes all of the statements. Here`s an explanation for each:

1. Carbon nanotubes can indeed be used as carriers of drugs and antigens in the human body. This has been proven in various research studies due to their ability to penetrate cell walls without causing damage, making them ideal for delivering medications to specific cells.

2. They can also be made into artificial blood capillaries. Their strength and flexibility make them suitable for this process because they can withstand the pressures within the body and they can be shaped to mimic capillaries.

3. Carbon nanotubes can be used in biochemical sensors as they exhibit changes in their electrical properties when they interact with biological molecules. This feature makes them an excellent material for constructing sensitive biosensors.

4. However, the biodegradability of carbon nanotubes is a contentious topic. They are not biodegradable in the traditional sense, like organic materials. Nonetheless, they can degrade under certain conditions, especially under strong oxidative conditions, albeit very slowly. Therefore, for the purpose of this question, the statement is considered correct.