<PAGE>   1
 
                                                                    EXHIBIT 99.3
 
                          AMERICA WEST AIRLINES, INC.
 
                               OFFER TO EXCHANGE
                   PASS THROUGH CERTIFICATES, SERIES 1998-1,
                           WHICH HAVE BEEN REGISTERED
                 UNDER THE SECURITIES ACT OF 1933, AS AMENDED,
                          FOR ANY AND ALL OUTSTANDING
                    PASS THROUGH CERTIFICATES, SERIES 1998-1
 
To: Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:
 
   
     Upon and subject to the terms and conditions set forth in the Prospectus,
dated March 26, 1999 (the "Prospectus"), and the enclosed Letter of Transmittal
(the "Letter of Transmittal"), an offer to exchange (the "Exchange Offer") the
registered Pass Through Certificates, Series 1998-1 (the "New Certificates") for
any and all outstanding Pass Through Certificates, Series 1998-1 (the "Old
Certificates") is being made pursuant to such Prospectus. The Exchange Offer is
being made in order to satisfy certain obligations of America West Airlines,
Inc. (the "Company") contained in the Exchange and Registration Rights Agreement
dated as of October 6, 1998, between the Company and the Initial Purchasers.
    
 
     The CUSIP numbers for the Old Certificates are as follows: Class A (023654
AK 2), Class B (023654 AL O), and Class C (023654 AM 8).
 
     We are requesting that you contact your clients for whom you hold Old
Certificates regarding the Exchange Offer. For your information and for
forwarding to your clients for whom you hold Old Certificates registered in your
name or in the name of your nominee, or who hold Old Certificates registered in
their own names, we are enclosing the following documents:
 
   
          1. Prospectus dated March 25, 1999;
    
 
          2. The Letter of Transmittal for your use and for the information of
     your clients;
 
          3. A Notice of Guaranteed Delivery to be used to accept the Exchange
     Offer if certificates for Old Certificates are not immediately available or
     time will not permit all required documents to reach the Exchange Agent
     prior to the Expiration Date (as defined below) or if the procedure for
     book-entry transfer cannot be completed on a timely basis; and
 
          4. A form of letter which may be sent to your clients for whose
     account you hold Old Certificates registered in your name or the name of
     your nominee, with space provided for obtaining such clients' instructions
     with regard to the Exchange Offer.
 
   
     Your prompt action is requested. The Exchange Offer will expire at 5:00
p.m., New York City time, on April 26, 1999 (the "Expiration Date") (30 calendar
days following the commencement of the Exchange Offer), unless extended by the
Company. The Old Certificates tendered pursuant to the Exchange Offer may be
withdrawn at any time before the Expiration Date.
    
 
     To participate in the Exchange Offer, a duly executed and properly
completed Letter of Transmittal (or facsimile thereof), with any required
signature guarantees and any other required documents, should be sent to the
Exchange Agent and certificates representing the Old Certificates should be
delivered to the Exchange Agent, all in accordance with the instructions set
forth in the Letter of Transmittal and the Prospectus.
<PAGE>   2
 
     Please note that brokers, dealers, commercial banks, trust companies and
other nominees who hold Old Certificates through The Depository Trust Company
("DTC") must effect tenders by book-entry transfer through DTC's Automated
Tender Offer Program ("ATOP").
 
     If holders of Old Certificates wish to tender, but it is impracticable for
them to forward their certificates for Old Certificates prior to the expiration
of the Exchange Offer or to comply with the book-entry transfer procedures on a
timely basis, a tender may be effected by following the guaranteed delivery
procedures described in the Prospectus under "The Exchange Offer -- Guaranteed
Delivery Procedures".
 
     Additional copies of the enclosed material may be obtained from Wilmington
Trust Company, the Exchange Agent, at 1100 North Market Street, Wilmington,
Delaware 19890-0001, Attention: Kristin Long, phone (302) 651-1562 and facsimile
(302) 651-1079.
 
                                                         AMERICA WEST AIRLINES,
INC.
 
                                        2