The bible's description of the church is full of "one anothers" and "each others" because God's intent is for the people of the church to be interdependent - all upon one another.
As we are interdependent within the body, we must also be totally dependent: upon the Holy Spirit. In fact, the above picture could be improved if the word "Holy Spirit" was placed in the middle. That would show that those who depend upon one another ultimately depend on the power of the Holy Spirit in order to function how God wants us to as His church.
How can we do this? How can we be dependently interdependent? I think the key is to put our pride to the side and be willing to be served by others and learn from others. As we do this, we will be built up and others will enjoy serving. At the same time, we should serve and teach one another. It "cuts both ways."
One of the reasons the traditional church of the West simply does not work is that we are too independent. We do not rely enough on the Holy Spirit or on our brothers and sisters. Let us strive to be dependent people.