1. INTRODUCTION  
2. SURVEYS TO CROSS-CORRELATE  
2.1 PAUS  
2.2 eBOSS/DESI  
3. SIMULATION OF THE SURVEY DATA  
3.1 Independent simulations  
3.2 Simulation of PAUS Ly 𝛼 IM  
3.3 eBOSS/DESI: Ly 𝛼 forest  
4. SIMULATED CROSS-CORRELATION ESTIMATOR  
4.1 Estimator definition  
4.2 Noise bias  
5. THEORETICAL CORRELATION FUNCTION  
5.1 Smoothing  
5.2 Monopole, parallel and perpendicular 2PCF  
5.3 Bias and RSDs  
6. RESULTS  
6.1 Cross-correlation without noise or foregrounds. Comparison against theory  
6.2 Cross-correlation with uncorrelated noise: Probability of detection  
6.3 Cross-correlation with correlated noise: Probability of detection  
7. CONCLUSIONS