Minimal Streams reproducer. Piping stream1 -> stream2 -> process.stdout works. Piping stream1 -> stream2 -> stream3 -> process.stdout does not work. Why?

streams-test.js

var Stream = require('stream');

var stream1 = new Stream;
stream1.readable = true;

var stream2 = new Stream;
stream2.readable = stream2.writable = true;

var stream3 = new Stream;
stream3.readable = stream3.writeable = true;

var i = 0;

stream2.write = function(data){this.emit('data', data)};
stream3.write = function(data){this.emit('data', data)};

setInterval((function() {
    stream1.emit('data', String(i++));
}), 100);
  
 //works:
  stream1.pipe(stream2).pipe(process.stdout);
 
 //does not work - why???
 //stream1.pipe(stream2).pipe(stream3).pipe(process.stdout);