How to send Serial data from an Arduino Uno into the Serial of an ESP-01?
Writing Junk From Memory
Serial.write(analogRead(A0) + &quot;\r\n&quot;);

This is advancing a pointer to &quot;\r\n&quot; by whatever number is being returned by analogRead.  In other words, you are not sending the measurement but junk from memory after (or sometimes at) &quot;\r\n&quot;'s memory location.
Serial.println(analogRead(A0)); appears to be what you were going for here.  println's line termination for the UNO serial connection is &quot;\r\n&quot;.
Logic Levels
When it comes to attaching the serial connections together, there should be some level conversion going on.  Because an UNO's pins are 5V logic levels and the ESP-01 expects 3.3v levels.